rm(list=ls())
library(plotly)
## Loading required package: ggplot2
##
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
##
## last_plot
## The following object is masked from 'package:stats':
##
## filter
## The following object is masked from 'package:graphics':
##
## layout
library(ROCR)
library(readr); library(dplyr); library(tidyr); library(ggplot2)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(rmarkdown)
library(GGally)
## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2
library(tree)
library(DataExplorer)
library(factoextra)
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library(randomForest)
## randomForest 4.7-1.2
## Type rfNews() to see new features/changes/bug fixes.
##
## Attaching package: 'randomForest'
## The following object is masked from 'package:dplyr':
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## combine
## The following object is masked from 'package:ggplot2':
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## margin
library(clValid)
## Loading required package: cluster
The data set is unstructured and we want to import data into a tidy format (i.e. dataframe)
# To input this unstructured file into R we use read_delim
Customers <- read_delim("/Users/ogheneatoma/Documents/ST309 final project - SmartRetail/data/marketing_campaign.csv", delim = "\t")
## Rows: 2240 Columns: 29
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: "\t"
## chr (3): Education, Marital_Status, Dt_Customer
## dbl (26): ID, Year_Birth, Income, Kidhome, Teenhome, Recency, MntWines, MntF...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
# To show # of observations and features in this data set
dim(Customers)
## [1] 2240 29
Now we have a tidy data set with each feature forming a column and each value having its own cell
Column names:
names(Customers)
## [1] "ID" "Year_Birth" "Education"
## [4] "Marital_Status" "Income" "Kidhome"
## [7] "Teenhome" "Dt_Customer" "Recency"
## [10] "MntWines" "MntFruits" "MntMeatProducts"
## [13] "MntFishProducts" "MntSweetProducts" "MntGoldProds"
## [16] "NumDealsPurchases" "NumWebPurchases" "NumCatalogPurchases"
## [19] "NumStorePurchases" "NumWebVisitsMonth" "AcceptedCmp3"
## [22] "AcceptedCmp4" "AcceptedCmp5" "AcceptedCmp1"
## [25] "AcceptedCmp2" "Complain" "Z_CostContact"
## [28] "Z_Revenue" "Response"
nunique <- function(x) length(unique(x))
nunique_counts <- sapply(Customers, nunique)
nunique_counts
## ID Year_Birth Education Marital_Status
## 2240 59 5 8
## Income Kidhome Teenhome Dt_Customer
## 1975 3 3 663
## Recency MntWines MntFruits MntMeatProducts
## 100 776 158 558
## MntFishProducts MntSweetProducts MntGoldProds NumDealsPurchases
## 182 177 213 15
## NumWebPurchases NumCatalogPurchases NumStorePurchases NumWebVisitsMonth
## 15 14 14 16
## AcceptedCmp3 AcceptedCmp4 AcceptedCmp5 AcceptedCmp1
## 2 2 2 2
## AcceptedCmp2 Complain Z_CostContact Z_Revenue
## 2 2 1 1
## Response
## 2
summary(Customers)
## ID Year_Birth Education Marital_Status
## Min. : 0 Min. :1893 Length:2240 Length:2240
## 1st Qu.: 2828 1st Qu.:1959 Class :character Class :character
## Median : 5458 Median :1970 Mode :character Mode :character
## Mean : 5592 Mean :1969
## 3rd Qu.: 8428 3rd Qu.:1977
## Max. :11191 Max. :1996
##
## Income Kidhome Teenhome Dt_Customer
## Min. : 1730 Min. :0.0000 Min. :0.0000 Length:2240
## 1st Qu.: 35303 1st Qu.:0.0000 1st Qu.:0.0000 Class :character
## Median : 51382 Median :0.0000 Median :0.0000 Mode :character
## Mean : 52247 Mean :0.4442 Mean :0.5062
## 3rd Qu.: 68522 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :666666 Max. :2.0000 Max. :2.0000
## NA's :24
## Recency MntWines MntFruits MntMeatProducts
## Min. : 0.00 Min. : 0.00 Min. : 0.0 Min. : 0
## 1st Qu.:24.00 1st Qu.: 23.75 1st Qu.: 1.0 1st Qu.: 16
## Median :49.00 Median : 173.50 Median : 8.0 Median : 67
## Mean :49.11 Mean : 303.94 Mean : 26.3 Mean : 167
## 3rd Qu.:74.00 3rd Qu.: 504.25 3rd Qu.: 33.0 3rd Qu.: 232
## Max. :99.00 Max. :1493.00 Max. :199.0 Max. :1725
##
## MntFishProducts MntSweetProducts MntGoldProds NumDealsPurchases
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.000
## 1st Qu.: 3.00 1st Qu.: 1.00 1st Qu.: 9.00 1st Qu.: 1.000
## Median : 12.00 Median : 8.00 Median : 24.00 Median : 2.000
## Mean : 37.53 Mean : 27.06 Mean : 44.02 Mean : 2.325
## 3rd Qu.: 50.00 3rd Qu.: 33.00 3rd Qu.: 56.00 3rd Qu.: 3.000
## Max. :259.00 Max. :263.00 Max. :362.00 Max. :15.000
##
## NumWebPurchases NumCatalogPurchases NumStorePurchases NumWebVisitsMonth
## Min. : 0.000 Min. : 0.000 Min. : 0.00 Min. : 0.000
## 1st Qu.: 2.000 1st Qu.: 0.000 1st Qu.: 3.00 1st Qu.: 3.000
## Median : 4.000 Median : 2.000 Median : 5.00 Median : 6.000
## Mean : 4.085 Mean : 2.662 Mean : 5.79 Mean : 5.317
## 3rd Qu.: 6.000 3rd Qu.: 4.000 3rd Qu.: 8.00 3rd Qu.: 7.000
## Max. :27.000 Max. :28.000 Max. :13.00 Max. :20.000
##
## AcceptedCmp3 AcceptedCmp4 AcceptedCmp5 AcceptedCmp1
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.07277 Mean :0.07455 Mean :0.07277 Mean :0.06429
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
##
## AcceptedCmp2 Complain Z_CostContact Z_Revenue
## Min. :0.00000 Min. :0.000000 Min. :3 Min. :11
## 1st Qu.:0.00000 1st Qu.:0.000000 1st Qu.:3 1st Qu.:11
## Median :0.00000 Median :0.000000 Median :3 Median :11
## Mean :0.01339 Mean :0.009375 Mean :3 Mean :11
## 3rd Qu.:0.00000 3rd Qu.:0.000000 3rd Qu.:3 3rd Qu.:11
## Max. :1.00000 Max. :1.000000 Max. :3 Max. :11
##
## Response
## Min. :0.0000
## 1st Qu.:0.0000
## Median :0.0000
## Mean :0.1491
## 3rd Qu.:0.0000
## Max. :1.0000
##
plot_missing(Customers)
Customers <- na.omit(Customers)
There are 24 observations dropped in the data set because of missing values.
Check if there are duplicated data on the same customer characterised by their ID.
duplicates <- Customers$ID[duplicated(Customers$ID)]
duplicates
## numeric(0)
No duplicates found.
Based on the outliers found in the summary statistics, we will examine
par(mfrow = c(1, 2))
hist(2021-Customers$Year_Birth)
hist(Customers$Income)
Based on the histogram plots, we can see the majority of individuals are aged below 80 and have an income level below 100,000. Hence we drop the unusual values.
Removing the outliers
Customers_cleaned <- subset(Customers, 2021-Customers$Year_Birth < 80 & Income < 100000)
This drops another 24 observations.
# Age category for each customer assuming the data was collected in 2021
Customers_cleaned$Age <- 2021 - Customers_cleaned$Year_Birth
# Cut into differnet age groups by generations for our analysis
Customers_cleaned$AgeCategory <- cut(Customers_cleaned$Age, c(0, 40, 56, 78), c('<40', '41-56', '>57'))
# Number of Children
Customers_cleaned$NumChildren <- Customers_cleaned$Kidhome + Customers_cleaned$Teenhome
# Total spending
Customers_cleaned$Spending <- Customers_cleaned$MntWines + Customers_cleaned$MntFruits + Customers_cleaned$MntMeatProducts + Customers_cleaned$MntFishProducts + Customers_cleaned$MntSweetProducts + Customers_cleaned$MntGoldProds
# Log transformation of highly-skewed spending variables
Customers_cleaned <- Customers_cleaned %>%
mutate(
log_Wines = log(1+MntWines),
log_Fruits = log(1+MntFruits),
log_MeatProducts = log(1+MntMeatProducts),
log_FishProducts = log(1+MntFishProducts),
log_SweetProducts = log(1+MntSweetProducts),
log_GoldProds = log(1+MntGoldProds),
log_Spending = log(1+Spending)
)
# Relationship
Customers_cleaned$Relationship <- ifelse(Customers_cleaned$Marital_Status %in% c("Married", "Together"), 1, 0)
Customers_cleaned$Relationship <- factor(Customers_cleaned$Relationship, levels = c(0, 1), labels = c("Not Partnered", "Partnered"))
# Education
Education <- c(Basic = "Bachelors", '2n Cycle' = "Bachelors", Graduation = "Graduate", Master = "Masters", PhD = "PhD")
Customers_cleaned$Education <- as.character(Education[Customers_cleaned$Education])
Customers_cleaned$Education <- factor(Customers_cleaned$Education)
# Number of years customers joined
Dt_Customer <- as.Date(Customers_cleaned$Dt_Customer, format = "%d-%m-%Y")
Year_Customer <- as.numeric(format(Dt_Customer, "%Y"))
Customers_cleaned$YearsJoined <- 2021 - Year_Customer
# Number of accepted campaigns out of 6 in total
Customers_cleaned$TotalAcceptedCmp <- Customers_cleaned$AcceptedCmp1 + Customers_cleaned$AcceptedCmp2 + Customers_cleaned$AcceptedCmp3 + Customers_cleaned$AcceptedCmp4 + Customers_cleaned$AcceptedCmp5 + Customers_cleaned$Response
# Remove redundant columns
Customers_cleaned <- subset(Customers_cleaned, select = -c(ID, Z_CostContact, Z_Revenue, Year_Birth, Marital_Status, Dt_Customer, Teenhome, Kidhome))
Convert all variables into numerical using label encoding.
# Examine data types of the columns
str(Customers_cleaned)
## tibble [2,198 × 35] (S3: tbl_df/tbl/data.frame)
## $ Education : Factor w/ 4 levels "Bachelors","Graduate",..: 2 2 2 2 4 3 2 4 4 4 ...
## $ Income : num [1:2198] 58138 46344 71613 26646 58293 ...
## $ Recency : num [1:2198] 58 38 26 26 94 16 34 32 19 68 ...
## $ MntWines : num [1:2198] 635 11 426 11 173 520 235 76 14 28 ...
## $ MntFruits : num [1:2198] 88 1 49 4 43 42 65 10 0 0 ...
## $ MntMeatProducts : num [1:2198] 546 6 127 20 118 98 164 56 24 6 ...
## $ MntFishProducts : num [1:2198] 172 2 111 10 46 0 50 3 3 1 ...
## $ MntSweetProducts : num [1:2198] 88 1 21 3 27 42 49 1 3 1 ...
## $ MntGoldProds : num [1:2198] 88 6 42 5 15 14 27 23 2 13 ...
## $ NumDealsPurchases : num [1:2198] 3 2 1 2 5 2 4 2 1 1 ...
## $ NumWebPurchases : num [1:2198] 8 1 8 2 5 6 7 4 3 1 ...
## $ NumCatalogPurchases: num [1:2198] 10 1 2 0 3 4 3 0 0 0 ...
## $ NumStorePurchases : num [1:2198] 4 2 10 4 6 10 7 4 2 0 ...
## $ NumWebVisitsMonth : num [1:2198] 7 5 4 6 5 6 6 8 9 20 ...
## $ AcceptedCmp3 : num [1:2198] 0 0 0 0 0 0 0 0 0 1 ...
## $ AcceptedCmp4 : num [1:2198] 0 0 0 0 0 0 0 0 0 0 ...
## $ AcceptedCmp5 : num [1:2198] 0 0 0 0 0 0 0 0 0 0 ...
## $ AcceptedCmp1 : num [1:2198] 0 0 0 0 0 0 0 0 0 0 ...
## $ AcceptedCmp2 : num [1:2198] 0 0 0 0 0 0 0 0 0 0 ...
## $ Complain : num [1:2198] 0 0 0 0 0 0 0 0 0 0 ...
## $ Response : num [1:2198] 1 0 0 0 0 0 0 0 1 0 ...
## $ Age : num [1:2198] 64 67 56 37 40 54 50 36 47 71 ...
## $ AgeCategory : Factor w/ 3 levels "<40","41-56",..: 3 3 2 1 1 2 2 1 2 3 ...
## $ NumChildren : num [1:2198] 0 2 0 1 1 1 1 1 1 2 ...
## $ Spending : num [1:2198] 1617 27 776 53 422 ...
## $ log_Wines : num [1:2198] 6.46 2.48 6.06 2.48 5.16 ...
## $ log_Fruits : num [1:2198] 4.489 0.693 3.912 1.609 3.784 ...
## $ log_MeatProducts : num [1:2198] 6.3 1.95 4.85 3.04 4.78 ...
## $ log_FishProducts : num [1:2198] 5.15 1.1 4.72 2.4 3.85 ...
## $ log_SweetProducts : num [1:2198] 4.489 0.693 3.091 1.386 3.332 ...
## $ log_GoldProds : num [1:2198] 4.49 1.95 3.76 1.79 2.77 ...
## $ log_Spending : num [1:2198] 7.39 3.33 6.66 3.99 6.05 ...
## $ Relationship : Factor w/ 2 levels "Not Partnered",..: 1 1 2 2 2 2 1 2 2 2 ...
## $ YearsJoined : num [1:2198] 9 7 8 7 7 8 9 8 8 7 ...
## $ TotalAcceptedCmp : num [1:2198] 1 0 0 0 0 0 0 0 1 1 ...
## - attr(*, "na.action")= 'omit' Named int [1:24] 11 28 44 49 59 72 91 92 93 129 ...
## ..- attr(*, "names")= chr [1:24] "11" "28" "44" "49" ...
# Identify categorical columns
categorical_cols <- sapply(Customers_cleaned, is.factor)
# Apply label encoding to categorical columns
Customers_cleaned[categorical_cols] <- lapply(Customers_cleaned[categorical_cols], as.numeric)
Subset the data frame used for PCA
Customers_PCA <- subset(Customers_cleaned, select = -c(Spending,MntWines,MntFruits,MntMeatProducts,MntFishProducts,MntSweetProducts,MntGoldProds,AcceptedCmp1,AcceptedCmp2,AcceptedCmp3,AcceptedCmp4,AcceptedCmp5,Complain,Response, AgeCategory))
Pick out on some key features for correlation analysis.
plot_correlation(Customers_cleaned)
plot_histogram(Customers_cleaned)
Now the columns of the data set contain the following variables.
names(Customers_PCA)
## [1] "Education" "Income" "Recency"
## [4] "NumDealsPurchases" "NumWebPurchases" "NumCatalogPurchases"
## [7] "NumStorePurchases" "NumWebVisitsMonth" "Age"
## [10] "NumChildren" "log_Wines" "log_Fruits"
## [13] "log_MeatProducts" "log_FishProducts" "log_SweetProducts"
## [16] "log_GoldProds" "log_Spending" "Relationship"
## [19] "YearsJoined" "TotalAcceptedCmp"
We examine the mean and variances of different variables
apply(Customers_PCA, 2, mean)
## Education Income Recency NumDealsPurchases
## 2.480437e+00 5.148159e+04 4.900773e+01 2.324841e+00
## NumWebPurchases NumCatalogPurchases NumStorePurchases NumWebVisitsMonth
## 4.084167e+00 2.633303e+00 5.815742e+00 5.345314e+00
## Age NumChildren log_Wines log_Fruits
## 5.207188e+01 9.517743e-01 4.683589e+00 2.244250e+00
## log_MeatProducts log_FishProducts log_SweetProducts log_GoldProds
## 4.130463e+00 2.540630e+00 2.244045e+00 3.126917e+00
## log_Spending Relationship YearsJoined TotalAcceptedCmp
## 5.623144e+00 1.645587e+00 7.972247e+00 4.440400e-01
apply(Customers_PCA, 2, var)
## Education Income Recency NumDealsPurchases
## 9.088115e-01 4.230185e+08 8.364920e+02 3.554877e+00
## NumWebPurchases NumCatalogPurchases NumStorePurchases NumWebVisitsMonth
## 7.255999e+00 7.765336e+00 1.044714e+01 5.816526e+00
## Age NumChildren log_Wines log_Fruits
## 1.363344e+02 5.602586e-01 3.244145e+00 2.458667e+00
## log_MeatProducts log_FishProducts log_SweetProducts log_GoldProds
## 2.413958e+00 2.747391e+00 2.524857e+00 1.644474e+00
## log_Spending Relationship YearsJoined TotalAcceptedCmp
## 2.149672e+00 2.289086e-01 4.712367e-01 7.777046e-01
PCA with standardised variables
PCA <- prcomp(x = Customers_PCA, scale = TRUE)
Table_PCA <- rbind(PCA$rotation, summary(PCA)$importance)
knitr::kable(Table_PCA, digits = 4, align = 'c')
| PC1 | PC2 | PC3 | PC4 | PC5 | PC6 | PC7 | PC8 | PC9 | PC10 | PC11 | PC12 | PC13 | PC14 | PC15 | PC16 | PC17 | PC18 | PC19 | PC20 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Education | 0.0099 | 0.2065 | -0.5445 | -0.1559 | 0.1085 | -0.2216 | -0.1056 | 0.4948 | 0.0411 | 0.4625 | 0.1228 | -0.2081 | 0.1508 | 0.0390 | 0.0357 | -0.0467 | 0.1170 | 0.0324 | -0.0546 | -0.0120 |
| Income | 0.3058 | -0.0130 | -0.2373 | 0.0273 | -0.0125 | 0.0062 | 0.0785 | -0.0277 | -0.1706 | -0.2592 | -0.0195 | -0.1899 | -0.1028 | -0.0239 | 0.0144 | 0.0783 | -0.3221 | 0.5816 | -0.4992 | -0.0278 |
| Recency | 0.0068 | 0.0058 | 0.0537 | 0.4368 | 0.6357 | -0.5579 | 0.2359 | -0.1628 | 0.0379 | 0.0114 | -0.0464 | 0.0174 | 0.0558 | -0.0055 | 0.0316 | 0.0091 | 0.0166 | 0.0137 | -0.0016 | 0.0010 |
| NumDealsPurchases | -0.0104 | 0.5535 | 0.1884 | 0.1225 | -0.0611 | 0.1792 | 0.2604 | 0.0198 | -0.2750 | 0.3564 | -0.0283 | 0.4273 | 0.1076 | -0.0857 | -0.0196 | 0.3061 | 0.0176 | 0.1707 | -0.0974 | 0.0317 |
| NumWebPurchases | 0.2254 | 0.3456 | 0.0570 | -0.0440 | -0.0460 | -0.0024 | 0.1143 | 0.0210 | 0.5452 | -0.1734 | -0.2162 | -0.1865 | -0.3156 | 0.0654 | -0.0310 | 0.2502 | 0.4719 | 0.0143 | -0.0894 | 0.0416 |
| NumCatalogPurchases | 0.2883 | -0.0400 | -0.0817 | -0.0631 | 0.0310 | -0.0747 | 0.0025 | -0.0931 | -0.2272 | 0.1560 | 0.1442 | 0.3138 | -0.5472 | 0.0117 | -0.2987 | -0.4736 | 0.2741 | 0.0679 | 0.0183 | 0.0312 |
| NumStorePurchases | 0.2760 | 0.0952 | -0.0613 | 0.1198 | -0.0464 | 0.0541 | 0.0156 | 0.2280 | -0.0446 | -0.4049 | -0.2024 | 0.2737 | 0.5321 | -0.0032 | 0.1097 | -0.4168 | 0.2877 | -0.0280 | -0.0678 | 0.0202 |
| NumWebVisitsMonth | -0.2080 | 0.3490 | 0.2718 | -0.2125 | 0.0135 | -0.1036 | -0.0231 | -0.0196 | 0.3465 | 0.1250 | -0.2421 | -0.0155 | -0.0225 | -0.0219 | -0.0248 | -0.5513 | -0.4183 | 0.1254 | -0.1139 | -0.0180 |
| Age | 0.0560 | 0.2103 | -0.3554 | 0.2673 | 0.0829 | 0.2143 | -0.5862 | -0.5450 | 0.1302 | 0.1267 | -0.1079 | 0.0727 | 0.0925 | 0.0206 | -0.0019 | -0.0034 | -0.0075 | -0.0333 | -0.0373 | 0.0008 |
| NumChildren | -0.1881 | 0.3819 | -0.0579 | 0.2206 | -0.0329 | 0.1862 | 0.2114 | -0.1085 | -0.4217 | -0.1310 | 0.0262 | -0.5757 | -0.1119 | 0.0523 | 0.0593 | -0.2670 | 0.1006 | -0.1977 | 0.0750 | -0.0507 |
| log_Wines | 0.3035 | 0.2296 | -0.1814 | -0.0297 | 0.0016 | -0.0413 | 0.0576 | 0.0507 | 0.0247 | -0.1875 | 0.0289 | 0.0269 | -0.0594 | -0.0208 | 0.0129 | 0.0618 | -0.3677 | 0.0669 | 0.6619 | 0.4367 |
| log_Fruits | 0.2709 | -0.1363 | 0.2068 | 0.0901 | 0.0083 | 0.0890 | -0.0546 | 0.0178 | -0.0075 | 0.2371 | -0.1709 | -0.3440 | 0.1942 | -0.6599 | -0.3819 | -0.0271 | 0.0736 | 0.0763 | 0.1005 | 0.0318 |
| log_MeatProducts | 0.3327 | 0.0417 | 0.0017 | 0.0007 | 0.0068 | -0.0278 | 0.0307 | 0.0760 | -0.0446 | 0.0424 | -0.0396 | 0.0287 | -0.0987 | -0.0675 | -0.0013 | 0.0606 | -0.3094 | -0.7196 | -0.4329 | 0.2344 |
| log_FishProducts | 0.2695 | -0.1488 | 0.2141 | 0.1147 | -0.0118 | 0.0889 | -0.0895 | 0.0444 | -0.0358 | 0.3071 | -0.1171 | -0.0792 | -0.1842 | -0.0560 | 0.8020 | -0.1110 | 0.0568 | 0.1016 | 0.0718 | 0.0370 |
| log_SweetProducts | 0.2682 | -0.1394 | 0.2127 | 0.1034 | -0.0303 | 0.0589 | -0.0170 | 0.0436 | -0.0954 | 0.2646 | -0.2998 | -0.1845 | 0.1568 | 0.7232 | -0.2875 | 0.0194 | -0.0603 | 0.0527 | 0.0725 | 0.0283 |
| log_GoldProds | 0.2452 | 0.0960 | 0.2511 | -0.0175 | 0.0071 | 0.0739 | 0.0515 | -0.1863 | 0.2328 | 0.0600 | 0.7900 | -0.1388 | 0.2740 | 0.1196 | 0.0185 | -0.1113 | 0.0374 | 0.0506 | -0.0916 | 0.0936 |
| log_Spending | 0.3395 | 0.1317 | -0.0207 | -0.0244 | -0.0030 | -0.0243 | 0.0374 | 0.0231 | 0.0425 | -0.0388 | 0.0567 | 0.0498 | -0.0278 | -0.0213 | 0.0079 | 0.0554 | -0.2085 | -0.1506 | 0.2244 | -0.8567 |
| Relationship | -0.0087 | 0.0305 | -0.0121 | 0.3209 | -0.7386 | -0.5750 | -0.0405 | -0.1074 | 0.0073 | 0.0603 | 0.0311 | -0.0156 | 0.0279 | -0.0284 | 0.0040 | -0.0051 | -0.0005 | 0.0026 | -0.0029 | 0.0038 |
| YearsJoined | 0.0454 | 0.2580 | 0.3823 | -0.2454 | 0.1398 | -0.3168 | -0.6075 | 0.1194 | -0.3588 | -0.2213 | 0.0528 | -0.0787 | -0.0273 | 0.0113 | 0.0038 | 0.1559 | 0.0934 | 0.0287 | -0.0160 | 0.0105 |
| TotalAcceptedCmp | 0.1269 | -0.0099 | -0.1227 | -0.6218 | -0.0252 | -0.2209 | 0.2584 | -0.5326 | -0.1693 | 0.0969 | -0.1893 | -0.0648 | 0.2478 | -0.0095 | 0.1363 | 0.0368 | 0.1395 | -0.0509 | 0.0187 | 0.0194 |
| Standard deviation | 2.8356 | 1.4195 | 1.2694 | 1.0745 | 1.0039 | 0.9764 | 0.9098 | 0.8908 | 0.7654 | 0.7058 | 0.6740 | 0.6399 | 0.5985 | 0.5555 | 0.5454 | 0.4990 | 0.4822 | 0.3183 | 0.2892 | 0.1316 |
| Proportion of Variance | 0.4020 | 0.1007 | 0.0806 | 0.0577 | 0.0504 | 0.0477 | 0.0414 | 0.0397 | 0.0293 | 0.0249 | 0.0227 | 0.0205 | 0.0179 | 0.0154 | 0.0149 | 0.0124 | 0.0116 | 0.0051 | 0.0042 | 0.0009 |
| Cumulative Proportion | 0.4020 | 0.5028 | 0.5834 | 0.6411 | 0.6915 | 0.7391 | 0.7805 | 0.8202 | 0.8495 | 0.8744 | 0.8971 | 0.9176 | 0.9355 | 0.9509 | 0.9658 | 0.9783 | 0.9899 | 0.9950 | 0.9991 | 1.0000 |
par(mfrow=c(1,1))
plot(Table_PCA['Proportion of Variance',], type = 'o', lwd = 5, col = 'blue', main = 'PC proportions of total variance', xlab = 'PC', ylab = 'Proportion of variance', axes = FALSE)
axis(1, 1:22)
axis(2)
Subset data based on chosen principle components
nf <- 3
Customers_clust <- as.data.frame(PCA$x[, 1:nf])
Customers_clust
## PC1 PC2 PC3
## 1 3.9652558507 0.6607660795 1.591087289
## 2 -3.4722319455 -0.5637275979 -1.280295584
## 3 2.7525441587 -0.5272958013 0.346571407
## 4 -2.7696208652 -1.3743700228 0.358376316
## 5 0.9804712402 0.3991332033 -0.358985060
## 6 1.3043261953 0.7752718737 -0.695340025
## 7 1.7635014298 0.9867400903 1.789659077
## 8 -1.6775500664 0.5132352056 -0.046602800
## 9 -3.3100178001 0.0092184102 -0.927981220
## 10 -5.2371345187 2.1713880533 -0.630846939
## 11 -2.7583928842 -1.2670179871 2.639190479
## 12 3.0727704667 -1.7675497202 0.389638943
## 13 -0.6628823181 1.7770652767 -1.160078604
## 14 -3.1233231557 -1.4913145552 2.000037785
## 15 4.3490029545 0.4297254486 -1.743673033
## 16 -2.4418583812 0.8571300131 1.337978396
## 17 0.1459414193 0.1781602009 0.948443732
## 18 3.2807940346 1.9827950135 -1.033565728
## 19 -1.3813658331 -1.2117437717 3.112212179
## 20 0.0861094993 -0.5663084787 2.151368758
## 21 0.3948656122 1.8400223737 0.507799695
## 22 -0.2380085608 2.5147646708 -1.974358636
## 23 0.7506349783 0.7904782225 -2.606283209
## 24 -0.0400413525 2.6691918008 1.031036764
## 25 -2.0793564504 -1.2896012972 1.295254019
## 26 -1.0689270439 1.4161170214 0.626544647
## 27 -1.2204921389 -1.4192669914 0.802735769
## 28 3.8320679761 -0.8615875584 -2.189351919
## 29 -3.2703833477 -1.8318789285 -0.040975723
## 30 0.7149510517 -1.4444126008 -0.033144327
## 31 -2.5362109581 0.1216694939 -0.268080246
## 32 0.2639791612 2.5550996165 -0.061173080
## 33 2.7759716973 -0.2836910516 -0.671063804
## 34 -3.0298300683 0.5323407943 -1.568173770
## 35 1.9512811569 1.4928263035 -1.646633103
## 36 -2.3616482565 -0.5448546901 2.127933991
## 37 -3.1067010992 -1.0000362343 -0.903058769
## 38 3.0366948807 0.5024741609 -1.315797012
## 39 3.5176639598 -0.2477920599 1.128202946
## 40 -3.4311141848 -0.1808012065 0.408315071
## 41 -3.8438867784 -0.7304714598 -0.058717800
## 42 -3.6090983316 -0.4405422702 0.263005781
## 43 3.3168335607 -2.6323457754 0.326287835
## 44 -1.8283387565 -0.9710529817 3.989211939
## 45 -2.7970650449 -0.3751827533 0.883062861
## 46 2.3199647051 4.2715463838 0.319473409
## 47 1.6994362337 -1.2208635346 -0.993822941
## 48 4.4979383887 -0.2173494688 -0.293133029
## 49 -2.5654134179 -0.8756450957 0.799293114
## 50 4.7962525906 -2.2585565999 -0.327759179
## 51 1.3023736277 1.7083868510 0.848313769
## 52 5.5294531310 -0.7422988021 -0.564586793
## 53 3.5742952709 -1.3039524227 0.241890829
## 54 -3.4675245542 -2.1046530642 -0.440502698
## 55 -0.7574797751 1.8736213376 -2.010978198
## 56 3.9284316382 -1.4812804902 -0.890546150
## 57 1.1613315592 1.0828610617 0.411106976
## 58 1.9430305829 1.9063147534 0.463937456
## 59 0.1029854272 1.2582772758 -2.818562120
## 60 2.9267132792 -0.6690004453 0.032050570
## 61 -3.2898821931 -1.2778443413 0.774527052
## 62 -5.3049942725 -0.7696054380 -1.353404816
## 63 4.3204903088 -0.3937320821 -0.083791812
## 64 2.1321285874 -0.1667907722 0.059107453
## 65 1.9493603831 2.1129303688 0.951018857
## 66 3.2150680577 -0.1169948105 -0.182887381
## 67 3.1168597406 1.6718619363 1.089078859
## 68 0.2722197198 3.0737577545 -0.945189855
## 69 -1.5415584479 -2.2350892518 -0.816528730
## 70 -4.1005463925 -1.1939571037 0.683086167
## 71 3.4672052838 -0.1674536762 0.294530419
## 72 4.6710489370 -1.1824525131 0.914396606
## 73 -3.8032017196 -2.5601412470 0.608395229
## 74 0.2985519516 1.6002732453 -0.654841405
## 75 -1.5335110931 0.7197432338 2.065867208
## 76 -4.2985570264 -1.0132464757 0.046364114
## 77 -2.5645026047 -0.0948997355 1.538538623
## 78 0.7149510517 -1.4444126008 -0.033144327
## 79 3.7073531223 -2.4271159647 -0.295169061
## 80 -2.8814013558 -0.0809374860 0.280798966
## 81 -2.8073961246 1.9759029336 -0.925877777
## 82 -0.2125333784 1.1994083583 -1.110535999
## 83 3.9888325987 -1.8923549644 0.054106400
## 84 -0.9666111741 -1.3506620426 -1.408350732
## 85 -3.5230685385 -1.0314564334 -1.172501864
## 86 -3.5619491751 -0.1141971477 -2.065962887
## 87 -2.9115198410 -1.7914938980 0.432485923
## 88 -0.2184611183 2.6220984515 0.097134421
## 89 -3.3217907419 0.2104560599 -0.397116953
## 90 3.4943581404 -0.7449525808 -0.318276869
## 91 1.1958287650 -0.7837369260 0.153094497
## 92 -2.8453463206 -0.1177074887 0.313069401
## 93 -3.1937742254 -0.1343205436 -2.162555348
## 94 3.9785206616 0.0759014664 1.383159346
## 95 2.9459476733 -0.0417911254 -1.054892748
## 96 3.7278268377 -2.1677911018 -1.279785478
## 97 -3.6299149037 -1.8375179393 1.341828645
## 98 -1.9800754070 1.5501458393 -0.317809383
## 99 2.5144881176 1.2396861196 1.348237705
## 100 -1.6006871168 0.1649056599 1.283658605
## 101 2.7632430131 -0.7336668036 -0.249508904
## 102 3.2665328169 -0.5877542262 0.473173948
## 103 2.6700828420 0.6013339036 0.738083362
## 104 -0.3670268129 1.7086521052 -1.889731798
## 105 3.4761069715 -1.4352659426 0.060937159
## 106 -0.4904133352 2.7655692723 -0.259865613
## 107 -2.3547512902 0.5408185017 -0.495907591
## 108 4.1222850381 -2.5421166383 -0.876024021
## 109 1.0979349262 1.0240563978 3.564964851
## 110 -2.5219242660 -0.4107839665 0.954382074
## 111 -3.3371827471 -1.1514004129 0.769039916
## 112 2.1451019118 1.0065526156 -0.077088803
## 113 -2.2561771054 -0.3849636826 -1.263255473
## 114 -4.0176397646 -0.1571722016 0.327151581
## 115 -3.3322778244 -1.0753349790 0.335755918
## 116 2.3797426127 -1.5797385704 0.917150833
## 117 3.5362847327 -1.7887947460 0.327957442
## 118 -3.0057138303 0.6293489413 -2.436838952
## 119 1.4382019094 1.5337263522 -2.215585317
## 120 1.6441636057 0.6889222964 0.766183334
## 121 0.0253696598 3.5204700813 -0.488007154
## 122 2.6944603803 -1.1090516375 0.125104110
## 123 -1.7958720798 2.8591966940 -1.071377860
## 124 2.7006178135 -0.7157587048 -2.131963312
## 125 -4.0618226731 -0.9608663264 2.565677154
## 126 -2.9763093280 2.0661494793 -1.285996507
## 127 -2.9324795256 -0.3322271912 -1.796261601
## 128 -3.4165423452 0.5689530638 -1.172016700
## 129 4.0784568572 -0.9895688269 0.422384119
## 130 1.1746004209 0.6015153156 -0.586947287
## 131 3.9737959275 -0.9543866291 -0.179411112
## 132 2.2818062962 1.1803550102 -0.429980446
## 133 -0.1179119742 -0.3855062806 2.204727670
## 134 0.9382327607 1.2875400421 1.610124738
## 135 -2.4321280385 -0.9431313519 1.497916514
## 136 -4.0552091495 -0.9594306302 0.378099088
## 137 -1.7414615045 2.9738334655 2.346251288
## 138 -0.6162592639 -2.0791388398 -0.999270200
## 139 0.8930438021 -0.1977835646 -1.775555645
## 140 0.7757600129 0.6920155949 -0.063764297
## 141 0.4287781900 1.2977573418 2.417264174
## 142 -1.9093338872 -0.9568516760 1.237849585
## 143 0.9684153127 2.6390515242 -1.930000954
## 144 3.3209569738 0.2132125984 -0.886809551
## 145 -0.5909894468 0.8162827002 -0.203732153
## 146 -4.1726674745 -0.7920528403 -0.872310755
## 147 -0.3579880768 -1.7435022247 0.105974556
## 148 3.4867547622 -1.4181245283 -0.393747588
## 149 -5.0226742219 0.5218709224 -1.260618478
## 150 3.3259832577 1.8124611784 -1.044649135
## 151 -2.3297664739 -0.0375841735 0.762149843
## 152 2.4464508082 -0.6316359332 -1.692925980
## 153 -2.5020862933 0.9943284167 0.300740300
## 154 2.1215367148 -1.2024143750 -0.284846667
## 155 -0.5753197159 -0.9634341009 -1.160433377
## 156 3.2767512218 -2.3620560576 1.345606563
## 157 -2.0339434607 -0.2681048543 0.038629901
## 158 -3.5037710468 -0.5160380834 -0.252288397
## 159 -2.7638575173 -0.7072509780 1.484792575
## 160 -1.7290807210 -0.3025237911 -0.566312362
## 161 -3.0336766973 0.5656765295 -2.952222761
## 162 -2.0687860172 -0.9215876780 -1.287952848
## 163 4.0260788633 1.1059503573 -0.075157626
## 164 4.6859105458 0.5022075197 -1.029454895
## 165 -3.8973142900 0.4599550682 -2.111521209
## 166 -4.6686882460 -1.1126314299 -1.755788396
## 167 3.4943581404 -0.7449525808 -0.318276869
## 168 -1.3475272866 -0.4349155637 -1.774383538
## 169 -2.7543853965 -1.4475533379 1.588275231
## 170 3.3696008563 -0.1029516327 -1.206057267
## 171 -3.3507601479 -0.9868991025 -1.015662939
## 172 -2.7704369342 -2.2869429481 0.708948897
## 173 -3.1677564692 -0.5983518326 1.693300507
## 174 -3.9036341629 -0.5361973340 -2.267217736
## 175 0.8762051640 0.8285550249 0.067409608
## 176 3.8652564840 -1.6593986579 -0.023690609
## 177 -3.0697531900 0.8661691201 -1.630985427
## 178 -2.7101614693 -1.2727964731 2.152018855
## 179 4.1285265136 -0.6137671561 0.134799647
## 180 -2.1237709382 -0.4695014769 1.527021506
## 181 -0.6136743525 1.2391646980 0.407291993
## 182 -3.9539294821 -0.0401647682 0.415809059
## 183 2.2085514439 -1.0074318943 -1.088857817
## 184 3.5781838719 -1.1264866712 -0.500212836
## 185 3.7415778051 -1.1455748228 -0.063675779
## 186 -1.0789945701 2.2919410914 -0.880672285
## 187 0.7039770325 0.9423306914 -1.200893505
## 188 3.6786906724 -1.7229238679 0.443811374
## 189 3.2002412419 0.9680757429 1.297290249
## 190 -3.8930979155 0.6999328325 -1.671344042
## 191 -3.0201074062 -1.6663540038 0.812074252
## 192 -2.8217172182 -1.1321253405 1.512781445
## 193 -0.0453037123 1.6470339743 0.380133521
## 194 -3.3167412283 -0.7206107820 -1.244958762
## 195 3.5823761834 2.9467907415 1.287755739
## 196 -0.1787307356 0.3616264148 0.190394831
## 197 3.1263691886 -1.6929677091 -1.478968556
## 198 -2.1230829091 4.1067254336 -0.423205036
## 199 -0.1630088796 3.9759948599 0.637544292
## 200 3.0887191041 -2.0534428030 0.747503464
## 201 0.4096798652 1.5378526643 1.398915552
## 202 -4.9429283408 -0.4711171237 -0.496374512
## 203 4.0930884560 -0.1452542326 -1.772725613
## 204 -1.2094556450 1.1268149563 -0.967550776
## 205 2.9307777616 1.2757881788 1.467995834
## 206 -1.4250737868 -2.3560162581 0.744935817
## 207 2.4877927894 -1.7222833212 -0.413724664
## 208 1.1024533527 0.8887591842 -2.673322444
## 209 -2.4896362944 1.3957844810 -0.802583299
## 210 2.9024348541 2.4494977086 1.003435788
## 211 -2.0313602438 0.9667268673 0.648755746
## 212 0.2250672387 1.5400363083 1.557902713
## 213 0.5712673475 1.9178066254 0.141166137
## 214 3.4960568403 -0.8179890014 -0.536330953
## 215 -4.5165264447 -1.2375724332 -1.280274789
## 216 -0.0444893781 3.1089027943 1.025643900
## 217 2.7477707609 -0.3735219668 1.039364073
## 218 -3.8041033292 -1.0748187850 0.416035870
## 219 -3.6760575904 -2.5209269373 -0.846152492
## 220 2.8082459059 1.3176599572 -1.016281905
## 221 -2.3564219884 -1.1041864798 1.768495451
## 222 -4.5026749752 -0.7048844433 -0.593799254
## 223 1.7063546635 0.1682042383 -2.047792132
## 224 -2.7996327272 -0.0920344034 1.600314317
## 225 4.2321746359 -1.1500531719 0.329236340
## 226 2.6897284103 0.0233739055 1.102959324
## 227 -4.1187611118 -0.6191424066 0.345801397
## 228 4.3534573460 -1.9382626323 0.675319934
## 229 1.5866400117 3.9178196860 0.799612634
## 230 -4.6317499686 0.0316170136 -2.429680562
## 231 2.4277530530 0.5174455324 -0.394109486
## 232 2.9160195968 0.8386991532 0.222869915
## 233 4.1550623247 -0.8675825177 0.725320642
## 234 3.1188321083 1.7321387578 1.193664811
## 235 -2.7343516708 -0.1689000751 0.296808149
## 236 -3.7008377204 -1.1513988867 0.856447630
## 237 -0.1822427364 -0.7003299903 2.169782103
## 238 2.3681177998 2.2128511938 1.278882175
## 239 -3.9309976486 0.1919668929 -0.974881945
## 240 1.5958715714 1.9732982999 -0.633066961
## 241 0.6551597038 0.1717245083 1.069044352
## 242 -3.1023667424 0.2073952435 0.747308508
## 243 -4.8460102401 0.9646253464 -2.031684899
## 244 -3.3644535448 -0.7812331414 1.544980702
## 245 1.4779686587 2.3036673766 -1.277902366
## 246 -0.5316587620 0.2336451341 -0.694131550
## 247 -3.8881441314 0.0189901043 -0.095719436
## 248 -1.0984735682 2.8768633507 -0.729934110
## 249 -2.2793552818 1.2518020181 -0.104310623
## 250 4.3237403333 -2.0704633107 -0.374767743
## 251 -1.7191420023 2.1927897453 -0.383285516
## 252 3.0870063787 -2.0552518000 0.699846559
## 253 -2.3950122314 -0.7261074308 0.750844542
## 254 3.0639820197 0.0910143404 1.128873429
## 255 -2.5247769419 -0.7581208787 -0.434982697
## 256 -1.0239811830 0.0333686602 -2.067019897
## 257 -2.9776227192 0.1493457989 -0.277265561
## 258 -2.2366818055 0.5147723985 0.393608249
## 259 1.5701048953 0.8284179767 -1.674624152
## 260 3.5766229988 -0.3193519552 0.936571224
## 261 2.2468887085 -2.6204431160 -0.549625231
## 262 2.6195851902 -1.4709983746 -1.181757758
## 263 1.9656284111 0.9486870018 -0.113828942
## 264 -1.9688589003 -0.9520899295 2.543016364
## 265 0.2250672387 1.5400363083 1.557902713
## 266 0.1459414193 0.1781602009 0.948443732
## 267 1.2146643497 -0.5925564104 -1.551965760
## 268 -3.8111942214 -0.1768763651 -1.741142097
## 269 -2.2994463731 -0.7438722120 0.907654271
## 270 3.7373501964 -0.7875206747 0.084429751
## 271 2.2471386157 4.3934121729 1.257881239
## 272 4.1456423356 -2.0516665795 -0.212954898
## 273 -0.1803730149 1.3685778527 -0.310435306
## 274 -2.6939659424 -1.8503667026 1.292022699
## 275 -1.6630077335 0.1405420536 0.661940635
## 276 4.1859432056 -1.1373902306 1.296716042
## 277 -3.2147108794 0.2821961933 0.730797947
## 278 -4.0586585052 -0.5594121133 -0.230160539
## 279 1.1140054748 2.2755677363 -1.074112023
## 280 -3.2982887822 -1.7021231981 1.569731613
## 281 -2.4661358234 -0.2143565583 0.095597834
## 282 2.1646032712 -2.1465665036 0.422738020
## 283 0.6301749540 2.4435849557 -2.565979045
## 284 -2.8659789652 0.5389787589 -0.852204125
## 285 1.1462530280 0.8524842206 0.123213252
## 286 -2.4771984448 -1.1676455279 -2.200585143
## 287 -0.4423954052 -0.2379908771 1.362940678
## 288 -2.7150057872 -0.1104810504 1.220485160
## 289 4.3128816749 -1.1283570144 -0.419204842
## 290 -1.6121753460 -1.0718765160 2.120874769
## 291 2.8343810306 -1.6291841835 -2.024477976
## 292 -0.5347042389 1.4096329938 -1.696594888
## 293 -0.4999573882 -1.2816102626 0.072548570
## 294 -2.8454032481 -0.6708648987 0.963936979
## 295 -4.3445165243 0.8168717587 -0.349659185
## 296 3.4661883846 -0.9533136973 -0.336889080
## 297 -1.3619785823 1.7023839840 -0.386409072
## 298 -4.1376980879 0.1113437564 -2.140829664
## 299 -2.4047740205 0.4746727637 0.444526533
## 300 1.2173278805 -0.6254026483 1.411126612
## 301 -3.6960736974 0.0237016290 -0.714513271
## 302 1.9661886804 -0.1421659022 0.073814120
## 303 -3.4454583459 -1.2406639968 0.743889507
## 304 -4.5546866224 -0.1959387196 -2.603345057
## 305 2.4397389036 2.3791178698 -0.055399127
## 306 0.9228854601 2.4483260748 0.908327333
## 307 2.4976673081 -0.6830084610 -0.412593802
## 308 -2.9622924445 0.4106421134 -0.159763449
## 309 -3.8389916451 -0.9700386715 0.155833147
## 310 -4.0102177031 0.7240430254 -3.204407841
## 311 -1.5667813236 0.6471751247 0.291683876
## 312 -4.1731205181 -1.0705774230 0.736155095
## 313 -2.3208013838 -1.6144215306 -0.753648863
## 314 1.0009408705 1.9088981038 -2.228954456
## 315 -2.5949342469 -0.5345156182 -0.630888057
## 316 -3.6948015037 -0.4868788021 0.930583584
## 317 2.9846156023 0.2592005190 0.821209102
## 318 4.3124516454 -0.1387893041 0.625820887
## 319 -2.7571980707 -0.4173039586 1.327589701
## 320 4.1718111418 -0.6143247189 -0.243686422
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## 1634 -2.3208013838 -1.6144215306 -0.753648863
## 1635 -2.1890585892 -1.4111435277 1.662877324
## 1636 1.6245483237 0.7532219565 -1.429581729
## 1637 -2.6049773554 0.0587497261 -1.573147220
## 1638 2.7834426184 1.3260677193 -0.378532140
## 1639 4.4768645940 1.3012865097 -0.910376734
## 1640 -0.6068353222 -0.0602252014 -0.945730195
## 1641 3.9579435187 -1.1421351958 -0.235922639
## 1642 3.8823659684 -0.3757030120 0.130231896
## 1643 3.5066626323 -1.0414142230 0.401464558
## 1644 4.4137139628 1.3916864899 1.657686364
## 1645 -1.7415107411 -2.3773645467 2.471167941
## 1646 -0.6881718839 0.5137713063 1.657943794
## 1647 -3.7384318423 -1.6081223121 1.923131975
## 1648 -1.0533436384 1.4015620299 -1.502290600
## 1649 -2.6541965045 -1.3109368021 0.048357568
## 1650 4.2520035653 -1.4606830308 0.662539387
## 1651 -1.7111624039 0.2431000937 0.212705053
## 1652 -3.7021861780 1.8217819990 -1.299254907
## 1653 -4.6987974120 -1.7911081862 -2.037626222
## 1654 -0.3609760849 0.4544809193 -0.368482099
## 1655 -3.7364048697 -0.7435676488 -1.155107492
## 1656 3.6099671218 -1.0366825973 0.282160467
## 1657 1.1920677479 2.1977262484 -0.062696423
## 1658 2.8020317938 1.0668793277 1.254335567
## 1659 3.9101037716 -2.1161835832 0.755552547
## 1660 0.5680134957 1.8055747735 -0.181449539
## 1661 3.0358727830 -0.6513032443 1.002566459
## 1662 -4.5854939997 -0.4057886609 -0.552196906
## 1663 -3.6865410023 -1.4281655525 2.454401780
## 1664 -2.4289872399 -1.2263634795 2.319925682
## 1665 2.4075079892 -0.4521704609 -0.290710455
## 1666 -3.9520185766 -0.1915422057 1.141195138
## 1667 2.0769082465 -1.6436549535 -1.362564825
## 1668 -4.2432500343 0.8378936751 -1.753295440
## 1669 3.7884617735 0.9383646902 -0.559171680
## 1670 2.5328163337 2.0720843940 1.830187728
## 1671 -3.5550399400 1.0533447877 -1.994315694
## 1672 -2.7447188136 -0.7629312820 1.645977514
## 1673 -0.3206438026 2.4599770090 -2.042822379
## 1674 -2.0046450083 0.2498037252 2.900254727
## 1675 -1.8512218718 0.3857366414 -0.588051851
## 1676 2.7617019524 2.1195833180 -0.465272017
## 1677 -0.3691135468 0.7417685631 0.821663494
## 1678 1.7307109925 -0.4652183742 0.204539267
## 1679 -0.3384423443 -0.9201488177 -1.923063366
## 1680 4.8581237357 -2.0256966504 -0.918505702
## 1681 3.5087865476 0.6254110060 -1.653555072
## 1682 -2.5156659729 -1.0923625656 0.148766346
## 1683 4.3885063486 -0.7764023061 0.499923050
## 1684 -2.6687219142 -1.9372523689 1.987323900
## 1685 0.5012142714 1.7069320883 3.185780453
## 1686 2.1373838834 0.2795157868 0.361276104
## 1687 -3.7496508324 -0.6744193543 0.269378945
## 1688 -1.0616795459 1.3971194023 1.075157084
## 1689 2.6385097276 1.7579685242 0.344935802
## 1690 -4.8086754648 -1.3136903268 0.844248896
## 1691 4.5323995616 -0.4126499685 -1.600632730
## 1692 4.8561938141 -1.8614168759 0.479393293
## 1693 4.4345771189 -1.0853363379 -2.087511894
## 1694 -0.8175271207 1.4450959366 -0.770326281
## 1695 -2.4445395422 -1.0161175689 -0.040409773
## 1696 -2.1340191471 2.6242746862 -0.560818412
## 1697 -2.7923709622 -1.2851288140 1.088678377
## 1698 2.6975763752 2.1219254549 -0.134050419
## 1699 3.8977273059 0.5412707054 0.238247186
## 1700 -3.3365819753 0.5697202846 -2.489219287
## 1701 -2.7233563842 -0.8765589489 1.384920072
## 1702 -3.1970433753 0.1503402029 -0.484949075
## 1703 4.3938673386 -2.0470282792 -0.488513691
## 1704 2.1424015438 -0.7810769822 0.659847929
## 1705 2.3306192110 1.2186402214 -0.567201747
## 1706 1.2956374804 0.5782397003 -0.340909847
## 1707 3.5871280774 -1.1979728260 -0.691046015
## 1708 0.1019621269 0.7253891487 -0.478374681
## 1709 -3.3442931546 -0.2282524811 -1.214778354
## 1710 -1.5243783884 0.0140650549 -0.921617911
## 1711 -0.1825030907 1.4774977017 1.431751444
## 1712 -0.8352400091 -0.4715016052 -1.812790164
## 1713 3.9576917599 -0.1884396300 -0.336750870
## 1714 0.2243663287 2.2818484168 -1.338698915
## 1715 4.3734757756 -0.9259464165 0.301925691
## 1716 -3.2290319812 -1.3208360022 1.326093111
## 1717 3.3696008563 -0.1029516327 -1.206057267
## 1718 2.8205899085 0.4819781234 1.174733105
## 1719 3.9765282424 -0.3435076788 -1.887365788
## 1720 1.7397679513 1.9620931634 -0.772153428
## 1721 -0.0535973950 1.4430179566 1.716292069
## 1722 -3.0042399858 -2.1249124402 1.144403353
## 1723 -0.2291687211 2.6489206835 -1.852523360
## 1724 -3.2993823020 0.6631578075 1.002082459
## 1725 -3.1176881942 -0.9473655187 1.574681029
## 1726 -2.4570217146 0.4814364317 0.304997019
## 1727 -1.5325861533 0.6645022139 -0.089083910
## 1728 -3.2999070039 0.0697966422 -2.652268420
## 1729 2.4289727043 0.1702584499 1.086971206
## 1730 2.2576568716 -0.1059171762 1.644775455
## 1731 -3.3193223879 -0.8415456667 1.644301142
## 1732 1.3473478682 -0.8789825336 0.445248131
## 1733 3.0747810402 0.0875499577 0.581832070
## 1734 -2.7999331688 -1.4205629353 2.016811533
## 1735 2.9622286281 1.2401689510 0.695808780
## 1736 -4.2073814439 -1.2943858022 -2.073258514
## 1737 3.3987709470 -2.4361691641 0.596489527
## 1738 -2.7704369342 -2.2869429481 0.708948897
## 1739 -1.4194288069 0.5088481086 -0.451475135
## 1740 -2.0432118083 0.9752979927 0.449334659
## 1741 -0.3452093894 0.0631030607 -1.471900494
## 1742 2.3677841467 -1.0396860943 0.434178212
## 1743 3.7753360944 -1.4219709721 -1.730077422
## 1744 -4.2851414488 -1.2197494527 -1.523105877
## 1745 -2.1340191471 2.6242746862 -0.560818412
## 1746 -1.5335110931 0.7197432338 2.065867208
## 1747 -1.3402237044 0.9639876510 -0.069594547
## 1748 -2.8164204370 0.3527894326 -1.416789428
## 1749 2.2914689018 -2.5966005339 1.200465677
## 1750 -3.0581811481 -1.2071572105 2.669916280
## 1751 -2.1578090439 0.5205844435 -1.553621332
## 1752 3.2119585730 0.2763142760 1.341842311
## 1753 2.2013249093 1.4041457845 0.240109799
## 1754 -0.6802897109 1.7535125026 0.800863929
## 1755 -1.2308709060 2.1144236216 0.980233759
## 1756 0.1167488352 1.8683844333 1.110495008
## 1757 -2.1019525843 -0.7096221049 0.617857263
## 1758 2.0225970149 3.8161366218 3.854220838
## 1759 3.2665328169 -0.5877542262 0.473173948
## 1760 -2.0530665573 0.2715250595 0.005046854
## 1761 -3.4472494557 0.0285259145 -3.063335794
## 1762 4.4401947386 -1.5452494896 0.041832211
## 1763 -2.0291800083 -1.4750013591 0.056937024
## 1764 -1.1378582615 1.8074950436 -0.032951458
## 1765 -3.6029304355 0.1085143406 -0.857029367
## 1766 0.9315941604 -0.5575330562 -0.476938619
## 1767 -2.3872954353 -0.6590348872 -0.566794883
## 1768 1.1301229169 0.1825733047 -0.667943077
## 1769 2.4369253143 -1.1015466813 0.679027088
## 1770 3.7065411106 -0.5321792816 0.308573025
## 1771 3.4469507811 1.2871857461 0.613302229
## 1772 -1.7375909786 1.1581228282 -1.525350104
## 1773 -0.0444893781 3.1089027943 1.025643900
## 1774 -3.7351774253 0.1767763269 -1.479984125
## 1775 1.7419336485 1.6932412686 -0.072024427
## 1776 0.5252605212 2.1792646351 -0.461489824
## 1777 -3.1023667424 0.2073952435 0.747308508
## 1778 3.6498893076 -1.9593035861 -1.381976779
## 1779 3.4205988142 -0.6875049063 -0.168527319
## 1780 -3.9549411663 0.7060055425 0.124679493
## 1781 1.1544176803 2.9363427528 0.578111599
## 1782 2.3188894195 -1.6470516148 -1.669500431
## 1783 2.7490609010 -1.6068187093 1.959320453
## 1784 3.5247157418 -0.0861608496 0.350722066
## 1785 -4.5136320753 -0.1833126666 -0.820988988
## 1786 2.3530864355 -0.0957490207 1.721398473
## 1787 3.7537756402 -0.2900873745 0.398769424
## 1788 0.6305293379 1.3861835171 0.029224511
## 1789 -5.1147961957 -0.2495247710 -2.460927974
## 1790 2.0780594521 -0.1586682189 -0.100614545
## 1791 -3.5872033575 0.6494535930 -1.129561928
## 1792 -2.1489226976 0.6973931276 -0.339743103
## 1793 2.9828913057 -0.1955742765 0.650862230
## 1794 3.2212065055 0.2707700769 3.074438597
## 1795 -3.7353747220 -0.5194968460 0.148490087
## 1796 0.1881430008 0.7286022534 -1.013151232
## 1797 3.4508140955 -1.7947533193 0.732780963
## 1798 3.8235859179 -0.8716075634 -1.477869721
## 1799 -1.1893185967 0.2450236536 1.372831233
## 1800 -2.1396167077 -0.3302531381 1.563105761
## 1801 -1.6457357742 1.0175460897 -0.284003469
## 1802 2.0995960209 2.9132938847 -0.308047555
## 1803 -0.8489064444 -0.0240774067 0.255497221
## 1804 -0.6767270781 0.2024566964 0.361169508
## 1805 -2.5240344628 0.4874017102 0.489257642
## 1806 4.1376048285 -1.5214516977 -1.165350357
## 1807 -0.7036754008 0.8384882775 -0.437442445
## 1808 0.7971379574 1.0925662232 1.142638174
## 1809 3.3157600747 4.4400513684 0.722446465
## 1810 -1.9972175831 0.9537760748 -0.105220709
## 1811 4.1411056016 -1.4905535922 -1.358629943
## 1812 -3.4356840252 -0.7950471287 -0.964186518
## 1813 2.9395631524 -1.0169201687 -0.438901362
## 1814 -0.0009284632 2.1848089456 -0.387922135
## 1815 2.9292371286 0.1042052632 -1.337406910
## 1816 -6.8295483456 5.2541656033 0.914713136
## 1817 -2.3677740139 -1.9360108271 1.599834167
## 1818 -0.0836109629 1.4384110939 -1.796251933
## 1819 -3.6323547902 -1.5181369498 1.004010068
## 1820 4.4507288421 -0.9977855100 1.867176640
## 1821 -4.5586570858 -1.1702580912 0.620456982
## 1822 3.5253477185 -0.6755448131 -0.200203459
## 1823 2.3050846891 -0.9107022586 -0.611613356
## 1824 3.4210403939 -0.5016256152 -0.523616560
## 1825 1.8242036198 2.2218007322 -1.464171278
## 1826 -2.1971618159 1.3123630084 -0.806559313
## 1827 -2.1813333002 -0.9469979069 0.381322339
## 1828 3.9065176023 -1.3639673092 -1.188239287
## 1829 1.2772779710 0.8000935043 2.165398425
## 1830 1.7933043961 0.2689325026 -0.747821089
## 1831 -4.6163880763 -2.3966106119 1.374670959
## 1832 1.3222307112 -1.0779911155 0.822742099
## 1833 2.5909413951 -1.0957768283 0.569550838
## 1834 3.6305587229 -0.6236962189 1.091401644
## 1835 0.9044863992 4.4319408913 1.503479215
## 1836 -2.9707840605 0.4992383431 -0.581885284
## 1837 -3.9503002154 -1.9268869356 -0.161576325
## 1838 -1.1714982866 2.7426029501 0.923186584
## 1839 5.2612354365 -2.1795872162 0.158967042
## 1840 -3.0794794627 -0.5106367165 -1.380571406
## 1841 3.6153708784 -0.1326167688 0.828440038
## 1842 -3.4949310572 -0.2006208492 -0.775351347
## 1843 0.9640350298 2.7708783198 -1.601888598
## 1844 -2.7138029067 -2.0576660305 -1.692317576
## 1845 -3.0972394599 -2.7783524587 1.594057571
## 1846 2.3411287130 1.3194595161 2.017117220
## 1847 4.4374639348 -2.0496324221 -0.356209063
## 1848 2.8976076704 1.1003675237 -1.694415157
## 1849 3.0362256513 0.7598874520 1.142877211
## 1850 3.2877104278 -0.2984176510 0.376874586
## 1851 -3.4957750098 -0.3113573064 -1.956693518
## 1852 -2.4376451947 0.4665734357 -2.215932535
## 1853 2.9733424483 -0.3397025661 -0.619992205
## 1854 -3.1351828813 -2.5816398580 -1.590792335
## 1855 0.7807817289 0.3814828999 1.901666298
## 1856 -3.2720907928 -0.2049398036 -2.727829282
## 1857 3.9577273459 -1.1379336108 -1.121032887
## 1858 2.4981092965 1.1993207021 0.975247753
## 1859 0.3882511111 -0.0849604987 1.037429554
## 1860 4.1550623247 -0.8675825177 0.725320642
## 1861 4.9150795570 -2.1170065246 -0.593117029
## 1862 -2.8064842947 -0.5978638520 1.064792790
## 1863 0.4287386632 3.0661832401 -0.513377325
## 1864 2.2319296121 -2.5736576869 -0.022523500
## 1865 -0.1769074392 -0.0446190763 -0.045545019
## 1866 -2.7101614693 -1.2727964731 2.152018855
## 1867 3.7643681544 -1.2710182195 -2.297780932
## 1868 1.2183822381 0.2527309653 -1.894095219
## 1869 -3.0697531900 0.8661691201 -1.630985427
## 1870 -3.0440013820 -1.9838019187 0.326011913
## 1871 1.0050044327 -1.8459649115 -1.088364264
## 1872 -3.2529712407 -0.2677802049 0.248536345
## 1873 -1.4586305950 -0.0983055294 -1.757423284
## 1874 2.8750201549 -1.6210774280 -0.023145731
## 1875 2.7493953684 1.2195517310 -0.522783778
## 1876 -3.0854574339 -0.9364589506 -0.102517132
## 1877 -2.6579451881 -1.3604061950 -0.178329293
## 1878 -3.1136375507 -0.6112721789 -0.133349162
## 1879 4.1119173873 -2.6161649285 -0.672548536
## 1880 3.3681174110 0.4202549274 1.264252811
## 1881 4.1212805021 -0.8628994499 0.017047256
## 1882 3.2865226748 1.1701706535 1.287451713
## 1883 0.7836735474 3.9263220105 -1.136482109
## 1884 0.0516814572 2.8991163177 0.468111480
## 1885 -2.4728729850 -1.7515693534 1.157444726
## 1886 -3.1292352366 0.0014754093 -0.830057184
## 1887 -1.2038744781 -1.7197464092 1.554740510
## 1888 -4.4895852933 0.6737511430 -1.159594620
## 1889 -2.2289287084 -2.2443762008 0.437564238
## 1890 3.0647440016 -0.9835001000 1.181535870
## 1891 4.5807004112 -0.6207366070 -0.538393500
## 1892 4.3242298800 -0.0861219002 -1.348310953
## 1893 3.4166375454 1.5968114223 0.223595629
## 1894 -3.7241848331 -1.3243515170 -0.213020605
## 1895 0.0509662855 2.5487011933 -1.346185274
## 1896 2.7032910950 -1.6051203717 0.171813424
## 1897 3.4706476797 0.1634953346 1.124092749
## 1898 1.6058338475 2.5710468173 0.420923444
## 1899 -2.2517069596 -0.0272852325 -1.688433070
## 1900 1.3171611324 0.4439228445 -1.499501512
## 1901 -3.0632625680 -0.6367429085 -0.092355722
## 1902 -2.8143456064 0.0840040234 -0.576939591
## 1903 3.3764085466 -0.0306392464 0.072616397
## 1904 -3.3396043262 -0.2307682500 1.609862932
## 1905 1.2947318968 0.9888499195 -1.163388195
## 1906 0.3752918863 2.7811598439 -1.468731309
## 1907 -4.2472767521 -1.3221922405 -2.032528280
## 1908 -3.0584035858 -1.8517518898 0.527424873
## 1909 3.2994196573 -0.9690170353 -2.482542970
## 1910 -3.2813766268 -0.3209041311 -0.312410913
## 1911 -3.4183444809 -0.6074153330 1.056207021
## 1912 4.0154998649 -2.3072727389 0.576741342
## 1913 -1.3768955815 0.3302558806 0.944354460
## 1914 3.1970342787 -0.6476252209 -0.009657616
## 1915 3.6542305823 -1.4443549542 1.613813284
## 1916 3.1382774056 -1.5917343860 -1.275326153
## 1917 -2.6748575698 0.4734686876 0.578705068
## 1918 -1.4098810496 0.0501085768 0.124980729
## 1919 1.7753203853 -0.7800285375 0.665180485
## 1920 3.6419307793 -1.4874018464 -1.014620995
## 1921 2.7496033074 0.8627846934 -0.558777866
## 1922 0.8671907957 -0.3691499977 -1.678976802
## 1923 3.1579787510 -1.7548361620 -2.745839383
## 1924 -4.0884251944 -1.6148955408 -0.568333360
## 1925 0.7064417606 1.5023379522 1.241612303
## 1926 4.5545473161 -1.6150416387 -0.196651013
## 1927 -1.2598392589 0.4702164947 -2.288382322
## 1928 3.2003677929 0.8242864426 0.336376030
## 1929 1.8931337147 0.7383234425 -2.286445770
## 1930 -3.0319657798 -0.7750635164 -0.880050961
## 1931 -1.3753432663 1.1814377239 0.411003526
## 1932 -2.1292646902 -0.3682146373 -0.810540688
## 1933 4.5341592769 -0.6662962371 -0.198589876
## 1934 2.5519188361 0.3325536545 1.055930550
## 1935 3.6072838999 -0.5551210935 -0.682974159
## 1936 4.3649682963 -1.4945668582 -0.562033928
## 1937 3.3828064783 -1.7597647273 -1.972509548
## 1938 1.3436880825 0.2005020711 -0.196427345
## 1939 -3.2470967570 -1.5929020643 -0.877210317
## 1940 -0.6802897109 1.7535125026 0.800863929
## 1941 0.3191537234 0.3490851335 0.979026342
## 1942 -0.6083383719 -0.1295572705 0.743311433
## 1943 0.0405416493 1.4001380054 1.045623611
## 1944 1.7481421306 -0.8351587012 2.396969848
## 1945 -2.9305541141 1.6860115339 -1.225124192
## 1946 -2.9131900120 -0.8951304210 -0.293852924
## 1947 -3.6022471718 -0.5338691757 0.540835858
## 1948 -1.1758393687 0.1161849345 2.285010197
## 1949 -2.0432118083 0.9752979927 0.449334659
## 1950 5.3104411978 -1.8267962762 -1.256616170
## 1951 -1.0773361363 -0.5045980898 -1.133586533
## 1952 -0.3390636890 2.7637226541 0.932403310
## 1953 -3.8438867784 -0.7304714598 -0.058717800
## 1954 -1.3526934633 2.0858515695 0.586759928
## 1955 0.7969833930 -1.7947896985 1.287754222
## 1956 -1.7321651328 -0.0129419567 1.697923443
## 1957 1.0023189549 -0.6333670367 -1.101963500
## 1958 3.9189670889 -0.5644542145 -1.367887459
## 1959 -0.9539085593 -0.0557035824 0.410235632
## 1960 4.9732094590 -0.0946017603 -1.744139948
## 1961 3.2609783215 -0.7429163483 -0.999633622
## 1962 -4.1954613959 0.1635263592 0.327472988
## 1963 3.9657031599 -2.2402787113 -0.423757120
## 1964 2.8625624423 -0.7933022045 0.904183314
## 1965 1.4154131713 0.6049935386 0.156412087
## 1966 -0.5455817683 2.0766618205 -0.587298272
## 1967 0.9732740370 -1.8659765344 0.947344576
## 1968 -3.6064284057 -1.2619105588 0.248883708
## 1969 -4.4076225927 -0.9207609627 -1.470145263
## 1970 -1.4419271609 0.1383229965 1.978512356
## 1971 -3.9454653050 -2.5787870265 -1.471731065
## 1972 -3.1199580716 1.0756217470 -0.938084275
## 1973 -3.6177020480 -0.1467822659 0.223142953
## 1974 3.3798884295 0.8747000587 1.851543873
## 1975 -0.7032407410 1.5997399838 0.135089779
## 1976 0.3590716832 -0.3623444885 -1.865367800
## 1977 1.6114558928 1.1325107821 -1.473149824
## 1978 3.6252446705 -1.0498662639 0.283013767
## 1979 -1.5859784756 0.1182343689 1.174285146
## 1980 4.9478742757 -1.2271300368 -0.484758169
## 1981 2.1485595223 1.1340967040 3.555327941
## 1982 4.0453048721 -0.5837022285 0.339649855
## 1983 -4.0679414570 -0.9815917885 0.584276772
## 1984 -2.2573320776 -1.6916469056 1.403619094
## 1985 -3.6966846640 0.5371956795 0.368570739
## 1986 -4.6681893615 -0.1438608207 -1.514130828
## 1987 -4.5896885104 0.5509631623 0.651452242
## 1988 -2.1891199587 -0.8980762848 0.534834295
## 1989 -1.9842872996 -0.9861578286 0.313634345
## 1990 -0.4592721285 1.1661774250 -0.123657052
## 1991 1.8027436932 0.5957417339 -2.006107901
## 1992 3.5080524695 1.1270310913 -0.785559576
## 1993 -2.7596843082 -1.1909539027 -0.669303992
## 1994 -4.0586585052 -0.5594121133 -0.230160539
## 1995 -2.5746909688 -1.5557870164 -0.277899442
## 1996 2.2993824243 2.6731962458 0.167960881
## 1997 -2.3560131888 -0.0063780275 3.739093241
## 1998 2.4250421925 1.8891432581 -1.925705100
## 1999 2.4192049865 1.0766662496 0.222710698
## 2000 -3.6182304287 0.0449210830 0.604682407
## 2001 3.3869025957 1.4243079266 1.964156786
## 2002 0.3561694632 -0.1418959569 1.766572504
## 2003 1.2139465571 -0.4473927237 -0.508378256
## 2004 3.1635289523 2.1282442153 1.921475304
## 2005 2.0527780457 0.3536513595 -0.159168676
## 2006 -2.4626274216 -0.9911202405 0.976820745
## 2007 3.8352301160 -0.3224013181 1.483374977
## 2008 2.2957409731 -1.4977262072 1.769973036
## 2009 2.6437306069 3.8551460036 2.106376678
## 2010 -2.9382759370 -1.1859247508 0.822155134
## 2011 -3.1561029804 -0.7224873829 -0.838236251
## 2012 0.8404390314 2.0750058200 2.724400163
## 2013 -0.5570280907 0.0818227391 0.983961335
## 2014 -1.9533382512 -0.5655338729 -1.811020119
## 2015 3.4868059688 -0.5101648409 -0.216288067
## 2016 2.9720696709 -0.2264194591 1.386681017
## 2017 3.7933626082 -1.2981909522 -0.340824668
## 2018 -3.2617861773 -0.3016108674 -1.040934900
## 2019 0.1672995947 2.4670124477 0.790751358
## 2020 2.3215344924 -0.7546469418 -0.581791657
## 2021 -3.5381366346 0.8670057814 -1.858791104
## 2022 -2.9916057161 -0.5352539588 -1.529032244
## 2023 -1.4372201300 -0.9637419096 1.225861538
## 2024 2.7042117305 0.8585133327 0.714333114
## 2025 3.1658438485 0.9052811622 -0.013271522
## 2026 1.7725498070 1.9820013433 -0.244074240
## 2027 -1.6630077335 0.1405420536 0.661940635
## 2028 3.2390065310 -1.1394687250 -0.280414060
## 2029 -3.7351314157 -0.3339873619 -0.666701640
## 2030 3.0963401858 1.7914210562 1.462965973
## 2031 2.4675256396 -0.4206736673 0.028012278
## 2032 -1.1248908459 -1.4613809791 -0.376922822
## 2033 2.2846849426 1.3007559564 -0.881057926
## 2034 -1.8440019464 -1.2178167723 0.698558184
## 2035 -3.0582100179 -0.9317868901 0.598487419
## 2036 0.7356651889 1.0677809199 -0.420218020
## 2037 2.7606037280 -0.5380265396 0.195958561
## 2038 -3.7353747220 -0.5194968460 0.148490087
## 2039 2.2249822436 -0.7394259970 0.487116725
## 2040 3.6339925230 -0.7710389773 1.566864828
## 2041 2.0958909110 -0.7870435950 -0.172917877
## 2042 -4.0373919246 -0.7137701075 -0.608560093
## 2043 -1.7524287175 -2.2990538366 0.867781792
## 2044 -1.1967628766 -0.0950210975 2.333427017
## 2045 0.0605008967 1.8892853777 1.232388848
## 2046 3.8746042999 -0.4807630394 0.878102472
## 2047 2.6131926577 0.8320261836 0.874325247
## 2048 2.9647932664 -1.7124987505 1.742066859
## 2049 3.9815543981 -1.0060256029 -1.011183166
## 2050 -2.4608911646 -1.3097117821 0.240706330
## 2051 -3.6095503030 -1.3090147276 -0.850415445
## 2052 -0.1768499645 2.5314004550 -0.059367190
## 2053 -3.8846584767 -2.0946501112 1.321707858
## 2054 1.0398632459 -1.4754105592 -0.354409543
## 2055 4.6059600898 -1.9302713462 1.376796756
## 2056 2.2993824243 2.6731962458 0.167960881
## 2057 -3.3845458123 0.2572267202 -2.457671992
## 2058 4.1696915335 -2.1818030924 0.796019667
## 2059 -0.7844392457 1.7304389800 0.088646981
## 2060 3.0613815566 1.0957155352 -0.056040305
## 2061 1.6917146059 -0.0218863853 0.667126495
## 2062 -3.3230281078 -0.7888119277 -1.768013150
## 2063 1.8665825190 0.6420421797 -3.237942789
## 2064 -3.1314515516 -0.4718612058 2.477819559
## 2065 2.6961947215 0.2333340877 -1.820429915
## 2066 -2.2103753386 -2.0211764105 1.980071868
## 2067 -2.8708198523 -0.9361309214 2.758636956
## 2068 -1.0773361363 -0.5045980898 -1.133586533
## 2069 1.1810094016 1.0747371960 0.142936003
## 2070 -0.8882242749 1.4612282896 -0.846736577
## 2071 4.2572922024 -0.6825584001 0.035518050
## 2072 1.3618546797 2.4926628495 0.974657214
## 2073 2.2918373642 0.7769201338 0.152327918
## 2074 -3.8317262543 -0.6669234990 -1.408246666
## 2075 -1.4083294215 -0.7586255636 0.031298500
## 2076 0.1980664435 2.1790158091 -0.076243126
## 2077 2.6624948828 0.4618965146 -0.505759722
## 2078 -3.1389859494 -1.4064670506 2.098173806
## 2079 2.9031176515 0.2400879654 -2.637225851
## 2080 4.0408379702 -1.1442230682 -0.505978793
## 2081 -3.5712448251 -0.8679823953 1.040688984
## 2082 -1.6340832196 0.1501648798 0.689802223
## 2083 -4.9407507154 -0.6798981861 0.708531579
## 2084 -2.2657621986 0.8009262844 1.123766851
## 2085 2.3598621942 0.9775996265 2.251488898
## 2086 -3.2526131695 -0.0473904215 -2.006981792
## 2087 4.3920196220 -1.0244969653 -0.421082144
## 2088 0.8762051640 0.8285550249 0.067409608
## 2089 2.9311936525 -0.8350855736 -1.568690419
## 2090 2.1369111736 1.7820791652 -0.692463107
## 2091 -5.3944164651 -0.0304566486 -0.253924661
## 2092 -3.3322778244 -1.0753349790 0.335755918
## 2093 2.4487356516 -0.9178063305 -1.705622024
## 2094 -2.7790581522 -0.5265189314 3.362565207
## 2095 2.5518031739 -0.8094147577 -1.014510722
## 2096 -0.0657409406 0.1438592858 -0.627532687
## 2097 -0.9457925630 1.3340827983 0.295866377
## 2098 -3.8271377451 -1.6126324226 0.076403899
## 2099 -0.3384519833 -1.2708317703 -2.104563788
## 2100 -1.7947591065 2.0554681211 0.741773483
## 2101 -4.2187476983 -1.5590022352 0.033816227
## 2102 -3.3559656836 -0.4242544674 -0.580679629
## 2103 -2.2468476676 0.9189708544 0.450774834
## 2104 -2.0909741871 -1.7899515172 0.070108691
## 2105 1.3412981049 2.1136197208 -0.341427372
## 2106 3.5264386626 -0.0702603205 -0.019814419
## 2107 -4.0116110961 -0.1790518272 -1.669456863
## 2108 -2.9161073653 1.2013208167 -1.479691294
## 2109 -0.1162850550 1.1829292567 -0.944258607
## 2110 -2.7191689899 -0.1937162279 -2.353562152
## 2111 -3.3818301655 0.7067047165 -1.508932218
## 2112 3.4072066995 -0.3869115490 1.382952898
## 2113 -2.5064884971 -0.3612021285 1.236951713
## 2114 -0.9457925630 1.3340827983 0.295866377
## 2115 -3.4342495676 -0.9184879674 -0.058819942
## 2116 -2.6079593656 -1.4531225222 0.614623739
## 2117 -1.2116634573 0.5417300652 0.739901845
## 2118 -3.2611160859 -1.8825101881 -1.381160562
## 2119 1.2470164107 0.9279206369 -2.354764344
## 2120 0.2807293675 -1.3593980587 -0.433171885
## 2121 3.5701208783 1.8681675940 0.195417423
## 2122 -0.1858052043 -0.6282026909 -0.153357183
## 2123 0.6623791364 1.4319496406 0.674866110
## 2124 4.3611727192 -0.9430641356 0.436531744
## 2125 -3.9809990447 -1.5956126339 2.177734520
## 2126 -2.7362033218 0.3636979084 -0.741150225
## 2127 3.5247157418 -0.0861608496 0.350722066
## 2128 2.8451143758 -1.5082114741 -0.997984426
## 2129 4.5899844734 -2.1035976399 0.605116736
## 2130 -2.9444056802 -0.8539024025 0.114845368
## 2131 0.7210673944 0.2635453652 -0.928830914
## 2132 2.8260001231 0.7444412963 0.287217204
## 2133 2.8902941581 -0.8480313767 0.673836234
## 2134 2.6289146531 0.5888451803 0.103250601
## 2135 0.7494188614 1.2573430706 -1.819548770
## 2136 4.5190491949 -0.9644995624 -1.050377087
## 2137 4.0175842422 -0.7676011911 0.434280807
## 2138 -0.2909789169 2.6491336138 0.184694865
## 2139 0.8491698954 0.5674631016 0.983262016
## 2140 -0.4324660132 0.1314697669 0.031537503
## 2141 -3.1166121336 0.2963181770 0.695119855
## 2142 -1.1500469112 2.5082861000 -1.537969192
## 2143 -0.8396558548 -2.5623084667 -0.122931390
## 2144 -2.2662348083 -1.3153401493 1.984971128
## 2145 -3.3413324947 -1.5777610889 -1.506615114
## 2146 3.1056292567 1.1343360552 0.254150071
## 2147 2.5288245167 -0.1470253890 -1.425664537
## 2148 4.2733878410 -0.8949644066 -2.312409147
## 2149 2.5335605858 -0.7455788020 -1.039761135
## 2150 -2.6676372477 -2.1275022762 0.462763817
## 2151 4.4004113717 -1.1891415655 -0.353472716
## 2152 -3.1891774979 -0.2158785772 0.178867912
## 2153 -3.8651115309 -1.1640551994 -0.363254338
## 2154 5.1052803221 -0.6343959179 0.804024963
## 2155 3.5668557775 1.3231393475 0.872018112
## 2156 -3.8736367474 1.4179556425 -0.353717473
## 2157 -1.2806142104 -1.4207454827 0.075762028
## 2158 0.9636916126 0.3760927684 0.433707840
## 2159 -0.1985713593 2.9153096636 -0.299026613
## 2160 -3.4900028735 0.7224561138 -0.252612927
## 2161 -2.2191396779 -1.2591363171 2.875547377
## 2162 2.1557558117 1.3477489725 1.272589705
## 2163 -0.1470825371 2.6379284773 0.045608397
## 2164 3.1860940921 -0.7738781483 0.756127584
## 2165 -2.4728729850 -1.7515693534 1.157444726
## 2166 -2.4797783193 2.7377547579 0.764269848
## 2167 2.3316259632 1.1437132806 2.385811682
## 2168 -3.6213863820 0.9501445875 -1.353709806
## 2169 -3.2189504164 -1.0630816194 1.838165591
## 2170 -3.3459407591 -0.0268111910 -0.845443352
## 2171 0.3485281893 2.1897938102 1.268866025
## 2172 3.5124472934 -1.6517066124 -0.061004172
## 2173 -3.5441245627 0.1662697310 -2.049992854
## 2174 3.4853422475 -1.8200980230 1.932245663
## 2175 -4.5880622878 -0.5710562165 1.313319103
## 2176 -4.2236372715 0.0854627696 -0.063214512
## 2177 -3.0314123755 -0.5360920966 1.008749274
## 2178 3.9873138038 -1.8513414954 -1.967074898
## 2179 -4.7225940819 -0.9626452024 0.200258543
## 2180 0.2691707977 1.3922542308 1.690820211
## 2181 1.1204562040 -0.2943990285 0.738033312
## 2182 3.9284316382 -1.4812804902 -0.890546150
## 2183 -2.9875007297 -0.4701000687 2.281780191
## 2184 -3.2012335538 0.4050796181 -1.523044123
## 2185 0.8654217679 0.8101318167 -2.209580159
## 2186 0.5909890805 3.0335309168 1.477352884
## 2187 0.7637774066 3.5558811704 1.622757106
## 2188 0.3169692393 1.3756157200 0.011940321
## 2189 -3.5404799578 -0.5562583787 0.187346988
## 2190 -2.6682146310 0.0839695260 1.581629015
## 2191 1.9041907564 1.4121932007 0.602560833
## 2192 -3.3564723314 -2.1711185516 1.109076641
## 2193 -3.4454583459 -1.2406639968 0.743889507
## 2194 2.6559170909 0.5366259407 1.175465353
## 2195 -1.3407201927 4.2745295166 -2.960382019
## 2196 2.2098320655 -1.3806840407 0.045170615
## 2197 2.7966772976 -0.0771899288 -1.270260193
## 2198 -1.3785120728 2.0657377203 -1.119772435
# Elbow method
fviz_nbclust(Customers_clust, hcut, method = "wss") +
geom_vline(xintercept = 4, linetype = 2) +
labs(subtitle = "Elbow method")
# Silhouette method
fviz_nbclust(Customers_clust, hcut, method = "silhouette") + labs(subtitle = "Silhouette method")
Step 1: preparing the data
Step 2: computing similarity information between every pair of objects in the data set
Step 3: using linkage function to group objects into hierarchical cluster tree
Step 4: determining where to cut the dendrogram into clusters
hc.complete = hclust(dist(Customers_clust), method = "complete")
hc_complete = cutree(hc.complete, 3)
table(hc_complete)
## hc_complete
## 1 2 3
## 996 894 308
fviz_dend(hc.complete, k = 3, # Cut in three groups
cex = 0.5, # Label size
k_colors = c("blue", "red", "green"),
color_labels_by_k = TRUE, # Colour labels by groups
rect = TRUE, # Add rectangle around groups
ylim = c(3,15)) # Zoom in the dendrogram
## Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
## of ggplot2 3.3.4.
## ℹ The deprecated feature was likely used in the factoextra package.
## Please report the issue at <https://github.com/kassambara/factoextra/issues>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
We do the k-means clustering to compare the clustering results we got from hierarchical clustering.
set.seed(123)
km = kmeans(Customers_clust, 3, nstart = 20)
km_clusters = km$cluster
km_clusters
## [1] 2 1 2 1 3 3 3 1 1 1 1 2 3 1 2 1 3 2 1 3 3 3 3 3 1 3 1 2 1 2 1 3 2 1 3 1 1
## [38] 2 2 1 1 1 2 1 1 3 2 2 1 2 3 2 2 1 3 2 3 3 3 2 1 1 2 2 3 2 2 3 1 1 2 2 1 3
## [75] 1 1 1 2 2 1 1 3 2 1 1 1 1 3 1 2 2 1 1 2 2 2 1 1 3 1 2 2 2 3 2 3 1 2 3 1 1
## [112] 3 1 1 1 2 2 1 3 3 3 2 3 2 1 1 1 1 2 3 2 3 3 3 1 1 3 1 3 3 3 1 3 2 3 1 1 2
## [149] 1 2 1 2 1 2 1 2 1 1 1 1 1 1 2 2 1 1 2 1 1 2 1 1 1 1 3 2 1 1 2 1 3 1 2 2 2
## [186] 3 3 2 2 1 1 1 3 1 3 3 2 3 3 2 3 1 2 3 2 1 2 3 1 3 1 3 3 2 1 3 2 1 1 2 1 1
## [223] 2 1 2 2 1 2 3 1 2 2 2 2 1 1 3 3 1 3 3 1 1 1 3 3 1 3 1 2 3 2 1 2 1 1 1 1 3
## [260] 2 2 2 3 1 3 3 2 1 1 2 3 2 3 1 1 2 1 1 3 1 1 2 3 1 3 1 3 1 2 1 2 3 1 1 1 2
## [297] 3 1 1 2 1 2 1 1 3 3 2 1 1 1 1 1 1 3 1 1 2 2 1 2 2 1 3 3 1 2 1 2 1 1 2 2 2
## [334] 2 3 1 1 2 2 3 2 3 1 1 3 3 2 1 2 3 1 3 1 3 1 1 1 1 2 1 1 1 3 3 1 1 3 2 1 3
## [371] 2 1 2 3 3 2 3 1 1 1 1 2 3 3 3 1 1 3 1 3 1 3 3 3 2 2 1 2 2 3 1 1 1 2 1 2 2
## [408] 1 2 2 3 3 2 1 1 2 3 1 1 1 1 1 1 1 1 3 2 1 3 2 2 1 2 3 3 2 3 3 2 3 2 1 2 1
## [445] 2 2 1 3 3 2 1 3 1 1 3 1 3 3 3 1 1 3 1 2 2 3 3 1 1 2 3 2 3 3 3 1 2 2 2 1 1
## [482] 1 3 1 2 2 2 1 3 1 2 3 2 3 2 1 1 2 2 1 2 3 2 1 1 2 2 2 3 3 2 3 3 1 3 1 2 3
## [519] 1 1 3 3 2 2 1 2 1 1 1 1 1 3 1 2 3 2 2 1 2 1 2 2 2 3 3 3 1 1 1 3 1 1 3 1 3
## [556] 1 1 1 3 1 3 1 1 1 1 2 2 3 1 1 2 2 1 2 1 1 1 1 1 1 3 2 3 1 3 1 1 1 2 3 3 1
## [593] 1 2 3 1 1 3 3 1 2 1 2 1 2 3 1 1 2 2 2 1 2 1 2 2 3 2 2 2 3 3 2 3 3 2 3 2 1
## [630] 3 1 3 1 3 2 3 3 1 2 1 1 1 1 1 1 3 2 3 2 2 3 1 3 2 1 2 2 2 3 3 2 2 2 2 2 3
## [667] 2 3 1 1 1 1 1 2 2 3 2 3 2 3 2 1 3 3 1 1 3 1 2 3 2 2 1 3 1 3 3 1 2 1 1 2 2
## [704] 3 2 1 3 3 3 2 2 2 2 1 2 3 1 1 1 2 2 1 2 1 2 2 3 2 2 2 2 3 3 1 1 1 3 2 1 2
## [741] 3 2 2 1 3 2 2 3 1 1 1 1 2 1 2 2 1 1 1 1 1 1 3 3 3 2 2 1 3 1 3 3 3 2 1 3 1
## [778] 3 2 2 3 1 3 3 2 1 1 2 3 2 3 1 3 3 1 2 1 3 1 2 2 3 1 2 1 1 3 3 1 1 2 3 2 1
## [815] 3 1 3 1 1 2 2 2 3 3 1 3 3 2 1 3 3 1 3 1 2 1 3 1 3 3 3 3 1 2 1 2 2 1 1 2 2
## [852] 3 1 2 1 1 1 1 1 2 2 3 1 3 2 1 3 2 1 2 3 2 2 3 1 2 1 2 2 3 2 2 1 1 1 2 2 3
## [889] 1 2 2 2 2 3 2 1 2 1 1 2 3 2 2 2 2 2 1 3 1 2 1 2 3 2 3 3 3 2 2 1 3 2 3 1 3
## [926] 1 1 3 1 1 1 3 3 1 3 2 3 1 1 3 2 2 1 1 3 2 1 1 3 2 2 2 3 1 3 1 1 1 2 2 3 2
## [963] 2 2 1 2 1 3 2 1 1 2 1 2 3 3 2 3 1 3 3 2 2 1 1 2 1 3 1 1 2 2 3 1 1 1 1 3 1
## [1000] 1 2 1 1 1 3 2 2 2 1 2 3 1 1 1 3 2 1 3 2 1 1 1 2 3 3 2 1 2 1 1 2 3 3 2 2 3
## [1037] 3 2 1 3 1 2 3 1 2 1 2 3 1 3 2 2 1 3 1 2 3 2 1 2 3 1 2 1 2 2 1 2 1 1 2 2 2
## [1074] 1 2 2 3 3 3 1 2 1 1 2 3 2 2 1 2 1 3 1 2 1 3 2 1 3 1 3 3 3 1 1 2 3 1 1 2 2
## [1111] 3 1 2 1 3 3 1 1 1 2 1 1 3 3 1 2 2 1 2 3 1 3 2 2 2 3 3 3 2 1 3 1 1 2 2 1 1
## [1148] 2 3 1 3 1 2 1 2 3 1 3 1 1 1 1 3 1 1 2 3 1 1 1 3 1 3 2 2 3 3 3 1 2 3 2 1 1
## [1185] 1 3 2 2 2 3 1 2 1 2 1 1 1 2 1 1 2 3 1 3 1 3 1 1 1 1 3 1 2 1 1 1 1 2 2 3 1
## [1222] 1 1 1 3 2 3 2 2 2 3 3 2 1 2 1 2 2 1 1 2 3 1 1 2 2 2 3 3 1 3 1 1 2 3 2 2 1
## [1259] 3 3 1 3 1 2 2 1 1 1 1 1 3 1 3 2 1 2 1 3 2 3 3 2 2 3 3 2 3 2 3 1 3 1 1 1 2
## [1296] 3 2 3 1 3 1 1 1 2 1 3 2 2 3 3 2 1 1 3 3 3 3 1 1 1 1 2 3 2 2 2 1 3 2 2 1 2
## [1333] 2 1 3 1 3 2 3 2 3 1 3 3 3 1 1 3 3 3 3 1 3 3 3 1 2 1 1 2 3 1 1 1 1 3 1 1 3
## [1370] 3 3 3 1 3 3 3 3 2 3 3 2 2 1 2 3 3 1 2 1 1 1 2 3 1 1 1 1 1 1 3 1 1 2 1 3 1
## [1407] 3 1 1 1 1 1 1 2 2 2 2 3 2 2 3 2 2 1 3 2 3 1 2 2 3 3 1 1 1 2 3 2 1 2 1 1 1
## [1444] 3 2 1 2 1 1 3 3 3 1 1 2 2 2 3 2 3 3 3 2 3 1 2 1 3 2 2 3 1 3 3 2 2 3 3 2 3
## [1481] 2 1 2 2 1 3 3 1 1 1 2 2 1 1 1 3 2 1 2 1 3 3 3 1 1 3 1 2 3 3 1 3 2 1 3 1 1
## [1518] 1 3 1 1 2 2 2 3 1 3 1 1 2 1 3 1 2 1 3 3 2 3 3 2 1 2 1 3 3 1 2 1 3 1 2 2 1
## [1555] 2 1 3 2 3 2 1 2 1 3 1 3 1 3 2 1 3 2 2 1 1 1 2 3 3 3 2 1 2 3 1 2 1 3 3 3 1
## [1592] 1 2 3 3 1 3 2 1 1 2 3 1 1 3 3 3 2 1 1 1 3 3 1 2 1 3 2 2 1 1 2 1 1 1 3 2 3
## [1629] 2 3 3 2 1 1 1 3 1 2 2 3 2 2 2 2 1 3 1 3 1 2 1 1 1 3 1 2 3 2 2 3 2 1 1 1 2
## [1666] 1 2 1 2 3 1 1 3 1 1 3 3 2 3 2 2 1 2 1 3 2 1 3 3 1 2 2 2 3 1 3 1 3 2 1 1 1
## [1703] 2 2 3 3 2 3 1 1 3 1 2 3 2 1 2 2 2 3 3 1 3 1 1 1 1 1 2 2 1 2 2 1 2 1 2 1 1
## [1740] 1 3 2 2 1 3 1 3 1 2 1 1 2 3 3 3 3 1 3 2 1 1 2 1 3 1 3 1 3 2 2 2 1 3 1 3 3
## [1777] 1 2 2 1 3 2 2 2 1 2 2 3 1 2 1 1 2 2 1 3 2 2 1 1 1 3 3 3 1 2 3 3 3 1 2 1 2
## [1814] 3 2 1 1 3 1 2 1 2 2 2 3 1 1 2 3 2 1 2 2 2 3 1 1 3 2 1 2 1 3 1 1 3 2 2 2 2
## [1851] 1 1 2 1 3 1 2 3 3 2 2 1 3 2 3 1 2 3 1 1 2 1 1 2 2 1 1 1 2 2 2 2 3 3 1 1 1
## [1888] 1 1 2 2 2 2 1 3 2 2 3 1 3 1 1 2 1 3 3 1 1 2 1 1 2 1 2 2 2 1 1 2 2 2 3 2 1
## [1925] 3 2 1 2 3 1 3 1 2 2 2 2 2 3 1 3 3 3 3 2 1 1 1 1 1 2 1 3 1 3 2 1 2 2 1 2 2
## [1962] 1 2 2 3 3 2 1 1 1 1 1 1 2 3 3 3 2 1 2 3 2 1 1 1 1 1 1 1 3 3 2 1 1 1 3 1 3
## [1999] 3 1 2 3 2 3 2 1 2 2 3 1 1 3 3 1 2 2 2 1 3 2 1 1 1 2 2 3 1 2 1 3 2 1 3 1 1
## [2036] 3 2 1 2 2 2 1 1 1 3 2 2 2 2 1 1 3 1 2 2 3 1 2 3 2 2 1 2 1 2 1 1 1 3 3 2 3
## [2073] 2 1 1 3 2 1 2 2 1 1 1 1 3 1 2 3 2 3 1 1 2 1 2 3 3 1 1 3 1 1 1 1 3 2 1 1 3
## [2110] 1 1 2 1 3 1 1 3 1 3 3 2 3 3 2 1 1 2 2 2 1 3 2 2 2 3 2 2 3 3 3 1 3 1 1 1 2
## [2147] 2 2 2 1 2 1 1 2 2 1 1 3 3 1 1 3 3 2 1 3 3 1 1 1 3 2 1 2 1 1 1 2 1 3 3 2 1
## [2184] 1 3 3 3 3 1 1 3 1 1 2 3 2 2 3
table(km_clusters, hc_complete)
## hc_complete
## km_clusters 1 2 3
## 1 24 832 20
## 2 700 0 0
## 3 272 62 288
hc_clusters = hc_complete
Append the result to our original dataset indicating which cluster each customer belongs to.
Customers_cleaned["kmcluster"] <- km_clusters
Customers_cleaned["hcluster"] <- hc_clusters
Customers_cleaned
## # A tibble: 2,198 × 37
## Education Income Recency MntWines MntFruits MntMeatProducts MntFishProducts
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2 58138 58 635 88 546 172
## 2 2 46344 38 11 1 6 2
## 3 2 71613 26 426 49 127 111
## 4 2 26646 26 11 4 20 10
## 5 4 58293 94 173 43 118 46
## 6 3 62513 16 520 42 98 0
## 7 2 55635 34 235 65 164 50
## 8 4 33454 32 76 10 56 3
## 9 4 30351 19 14 0 24 3
## 10 4 5648 68 28 0 6 1
## # ℹ 2,188 more rows
## # ℹ 30 more variables: MntSweetProducts <dbl>, MntGoldProds <dbl>,
## # NumDealsPurchases <dbl>, NumWebPurchases <dbl>, NumCatalogPurchases <dbl>,
## # NumStorePurchases <dbl>, NumWebVisitsMonth <dbl>, AcceptedCmp3 <dbl>,
## # AcceptedCmp4 <dbl>, AcceptedCmp5 <dbl>, AcceptedCmp1 <dbl>,
## # AcceptedCmp2 <dbl>, Complain <dbl>, Response <dbl>, Age <dbl>,
## # AgeCategory <dbl>, NumChildren <dbl>, Spending <dbl>, log_Wines <dbl>, …
PC1 <- Customers_clust[,1]
PC2 <- Customers_clust[,2]
PC3 <- Customers_clust[,3]
# Append the cluster result to our dataset
Customers_clust["hcluster"] <- hc_clusters
cluster3d <- plot_ly(Customers_clust, x = ~Customers_clust$PC1, y = ~Customers_clust$PC2, z = ~Customers_clust$PC3, color = ~as.factor(Customers_cleaned$hcluster), colors = c('#636EFA','#EF553B','#00CC96') ) %>%
add_markers(size = 12)
cluster3d <- cluster3d %>%
layout(
scene = list(
bgcolor = "#e5ecf6",
xaxis = list(title = "PC1"),
yaxis = list(title = "PC2"),
zaxis = list(title = "PC3")
)
)
cluster3d
Hierarchical Clustering Summary statistics
hcresult <- Customers_cleaned %>%
group_by(hcluster) %>%
summarise_all(mean) %>%
t() %>%
round(2)
hcresult
## [,1] [,2] [,3]
## hcluster 1.00 2.00 3.00
## Education 2.57 2.35 2.57
## Income 68695.69 32949.33 49606.84
## Recency 49.24 48.38 50.06
## MntWines 538.45 34.30 337.78
## MntFruits 49.72 4.06 15.06
## MntMeatProducts 314.15 18.36 109.38
## MntFishProducts 71.37 5.70 21.64
## MntSweetProducts 50.76 4.19 15.63
## MntGoldProds 66.53 13.13 60.17
## NumDealsPurchases 1.79 1.89 5.32
## NumWebPurchases 5.37 1.91 6.22
## NumCatalogPurchases 4.72 0.44 2.24
## NumStorePurchases 8.22 3.08 5.99
## NumWebVisitsMonth 3.71 6.53 7.20
## AcceptedCmp3 0.07 0.07 0.09
## AcceptedCmp4 0.12 0.01 0.09
## AcceptedCmp5 0.16 0.00 0.00
## AcceptedCmp1 0.13 0.00 0.02
## AcceptedCmp2 0.03 0.00 0.00
## Complain 0.01 0.01 0.00
## Response 0.20 0.08 0.19
## Age 54.10 49.10 54.14
## AgeCategory 2.28 2.01 2.32
## NumChildren 0.52 1.23 1.54
## Spending 1090.99 79.73 559.65
## log_Wines 6.05 2.87 5.53
## log_Fruits 3.34 1.16 1.86
## log_MeatProducts 5.42 2.62 4.36
## log_FishProducts 3.69 1.40 2.15
## log_SweetProducts 3.34 1.18 1.79
## log_GoldProds 3.80 2.19 3.67
## log_Spending 6.85 4.08 6.13
## Relationship 1.64 1.65 1.65
## YearsJoined 7.95 7.83 8.44
## TotalAcceptedCmp 0.71 0.17 0.40
## kmcluster 2.25 1.14 2.87
K-Means Summary Statistics
kmresult <- Customers_cleaned %>%
group_by(kmcluster) %>%
summarise_all(mean) %>%
t() %>%
round(2)
kmresult
## [,1] [,2] [,3]
## kmcluster 1.00 2.00 3.00
## Education 2.37 2.47 2.65
## Income 32699.80 73300.87 53377.64
## Recency 48.41 49.14 49.70
## MntWines 27.60 584.81 381.75
## MntFruits 3.85 62.85 16.76
## MntMeatProducts 16.01 397.85 113.31
## MntFishProducts 5.45 90.97 23.13
## MntSweetProducts 4.00 64.17 17.19
## MntGoldProds 12.21 74.90 53.71
## NumDealsPurchases 1.85 1.40 4.05
## NumWebPurchases 1.79 5.26 5.98
## NumCatalogPurchases 0.40 5.53 2.52
## NumStorePurchases 2.99 8.52 6.76
## NumWebVisitsMonth 6.50 3.05 6.31
## AcceptedCmp3 0.07 0.08 0.08
## AcceptedCmp4 0.01 0.11 0.12
## AcceptedCmp5 0.00 0.21 0.02
## AcceptedCmp1 0.00 0.17 0.03
## AcceptedCmp2 0.00 0.03 0.01
## Complain 0.01 0.01 0.01
## Response 0.08 0.24 0.15
## Age 48.98 53.08 55.29
## AgeCategory 2.00 2.22 2.37
## NumChildren 1.24 0.32 1.25
## Spending 69.12 1275.55 605.86
## log_Wines 2.79 6.20 5.64
## log_Fruits 1.11 3.76 2.14
## log_MeatProducts 2.56 5.79 4.48
## log_FishProducts 1.36 4.17 2.37
## log_SweetProducts 1.14 3.76 2.09
## log_GoldProds 2.15 3.95 3.57
## log_Spending 4.02 7.08 6.24
## Relationship 1.65 1.63 1.65
## YearsJoined 7.83 7.95 8.19
## TotalAcceptedCmp 0.16 0.83 0.41
## hcluster 2.00 1.00 2.03
From this, we can safely use the clustering result from Hierarchical Clustering.
barplot(table(hc_complete), main = "Number of customers in each cluster", xlab = "Clusters", ylab = "Counts")
Customers_cleaned$Education <- as.factor(Customers_cleaned$Education) # change in categorical variable
ggplot(Customers_cleaned, aes(x = hcluster, fill = Education)) +
geom_bar(position = "fill") +
labs(title = "Bar plot of education by cluster", x = "hcluster", y = "proportion")
mean_result <- aggregate(data = Customers_cleaned, Income ~ hcluster, mean)
sd_result <- aggregate(data = Customers_cleaned, Income ~ hcluster, sd)
count_result <- table(Customers_cleaned$hcluster)
# Combine mean, sd, and count into a single table
combined_table <- merge(merge(mean_result, sd_result, by = "hcluster"), as.data.frame(count_result), by.x = "hcluster", by.y = "Var1", all.x = TRUE)
# Rename the columns
colnames(combined_table) <- c("hcluster", "estimated_income", "sd_Income", "sample_count")
#calculate the standard error
combined_table$standard_error <- combined_table$sd_Income/ sqrt(combined_table$sample_count)
#calculate the t_score using 95% confidence interval
alpha = 0.05
degrees_of_freedom = combined_table$sample_count - 1
combined_table$t_score = qt(p=alpha/2, df=degrees_of_freedom,lower.tail=F)
#calculate the margin of error
combined_table$margin_error <- combined_table$t_score * combined_table$standard_error
#show the table result
combined_table
## hcluster estimated_income sd_Income sample_count standard_error t_score
## 1 1 68695.69 12793.98 996 405.3928 1.962351
## 2 2 32949.33 11696.60 894 391.1928 1.962624
## 3 3 49606.84 11566.32 308 659.0524 1.967721
## margin_error
## 1 795.5229
## 2 767.7643
## 3 1296.8314
ggplot(combined_table, aes(x = estimated_income, y = reorder(hcluster, estimated_income))) +
geom_errorbarh(aes(xmin = estimated_income - margin_error, xmax = estimated_income + margin_error)) +
geom_point(size = 3, color = "darkgreen") +
theme_minimal(base_size = 12.5) +
labs(title = "Mean customer household income",
subtitle = "For Each Hierarchial Cluster",
x = "Income Estimate",
y = "Cluster group")
numchildren <- Customers_cleaned %>%
group_by(hcluster) %>%
summarise(across(c("NumChildren"), mean))
numchildren_ct <- numchildren %>% gather(key = numchildren, value = Value, NumChildren)
ggplot(numchildren_ct, aes(x = factor(hcluster), y = Value, fill = numchildren)) +
geom_bar(stat = "identity", position = "dodge") +
labs(x = "Cluster Groups", y = "Total", title = "Average no. of Children") +
theme_minimal()
# Create a scatterplot
spending_plot <- ggplot(Customers_cleaned, aes(x = Spending, y = Income, color = as.factor(hcluster))) +
geom_point() +
labs(title = "Income and Spending for each Cluster") +
theme_minimal()
# Show the plot
print(spending_plot)
goods <- Customers_cleaned %>%
select(MntWines, MntFruits, MntMeatProducts, MntFishProducts, MntSweetProducts, MntGoldProds, Spending, hcluster)
sum_spending_by_commodity <- goods %>%
group_by(hcluster) %>%
summarise(across(c("MntWines", "MntFruits", "MntMeatProducts", "MntFishProducts", "MntSweetProducts", "MntGoldProds"), sum))
spending_by_cluster <- goods %>%
group_by(hcluster) %>%
summarise(across(c("Spending"), sum))
proportion <- sum_spending_by_commodity %>%
mutate(across(-1, ~./spending_by_cluster$Spending))
library(gt)
library(scales)
##
## Attaching package: 'scales'
## The following object is masked from 'package:readr':
##
## col_factor
spend_table <- proportion %>%
gt() %>%
data_color(
columns = c("MntWines", "MntFruits", "MntMeatProducts", "MntFishProducts", "MntSweetProducts", "MntGoldProds"),
colors = scales::col_numeric(
palette = "YlGn",
domain = NULL
)
)
## Warning: Since gt v0.9.0, the `colors` argument has been deprecated.
## • Please use the `fn` argument instead.
## This warning is displayed once every 8 hours.
spend_table
| hcluster | MntWines | MntFruits | MntMeatProducts | MntFishProducts | MntSweetProducts | MntGoldProds |
|---|---|---|---|---|---|---|
| 1 | 0.4935451 | 0.04557602 | 0.2879533 | 0.06541545 | 0.04652943 | 0.06098062 |
| 2 | 0.4301647 | 0.05089644 | 0.2302405 | 0.07149070 | 0.05249572 | 0.16471199 |
| 3 | 0.6035493 | 0.02690692 | 0.1954494 | 0.03866637 | 0.02792217 | 0.10750586 |
campaigns_plot <- ggplot(Customers_cleaned, aes(x = factor(TotalAcceptedCmp), fill = as.factor(hcluster))) +
geom_bar(position = "dodge") +
labs(title = "Count Of Promotion Accepted",
x = "Number Of Total Accepted Promotions") +
theme_minimal()
campaigns_plot
deals_plot <- ggplot(Customers_cleaned, aes(x = NumDealsPurchases, fill = as.factor(hcluster))) +
geom_bar(position = "dodge") +
labs(title = "Count of Deals Puchased",
x = "Number Of Deals Purhcased") +
theme_minimal()
deals_plot
sum_spending_by_commodity <- Customers_cleaned %>%
group_by(hcluster) %>%
summarise(across(c("NumWebPurchases", "NumCatalogPurchases", "NumStorePurchases"), mean))
purchases_ct <- sum_spending_by_commodity %>% gather(key = Purchases, value = Value, NumWebPurchases:NumStorePurchases)
ggplot(purchases_ct, aes(x = factor(hcluster), y = Value, fill = Purchases)) +
geom_bar(stat = "identity", position = "dodge") +
labs(x = "Cluster Groups", y = "Average Counts", title = "Average Counts of Purchases by Sales Channels") +
scale_fill_manual(values = c("NumWebPurchases" = "blue", "NumCatalogPurchases" = "green", "NumStorePurchases" = "red")) +
theme_minimal()
To maintain the consistency of our analysis, we should use the same variables that we used in the clustering analysis.
Customers_PCA["hcluster"] <- hc_clusters
Customers_PCA <- Customers_PCA %>%
mutate(
InCluster1 = as.factor(if_else(hcluster == 1, 1, 0)),
InCluster2 = as.factor(if_else(hcluster == 2, 1, 0)),
InCluster3 = as.factor(if_else(hcluster == 3, 1, 0)))
Tree for classifying cluster 1
# Fit a tree for cluster 1
tree1.Customers = tree(formula = InCluster1~.-InCluster2-InCluster3-hcluster, data=Customers_PCA)
plot(tree1.Customers)
text(tree1.Customers, pretty=1, cex = 0.7)
cv1.Customers = cv.tree(tree1.Customers, FUN=prune.misclass)
cv1.Customers$size
## [1] 10 9 8 6 3 2 1
cv1.Customers$dev
## [1] 177 177 190 190 231 265 996
# Prune the tree for cluster 1
prune1.Customers = prune.misclass(tree1.Customers, best=6)
plot(prune1.Customers)
text(prune1.Customers, pretty=1, cex = 0.7)
Tree for classifying cluster 2
# Fit the tree for cluster 2
tree2.Customers = tree(formula = InCluster2~.-InCluster1-InCluster3-hcluster, data=Customers_PCA)
plot(tree2.Customers)
text(tree2.Customers, pretty=1, cex = 0.7)
cv2.Customers = cv.tree(tree2.Customers, FUN=prune.misclass)
cv2.Customers$size
## [1] 5 2 1
cv2.Customers$dev
## [1] 118 118 894
# Prune the tree for cluster 2
prune2.Customers = prune.misclass(tree2.Customers, best=2)
plot(prune2.Customers)
text(prune2.Customers, pretty=1, cex = 0.7)
Tree for classifying cluster 3
# Fit the tree for cluster 3
tree3.Customers = tree(formula = InCluster3~.-InCluster1-InCluster2-hcluster, data=Customers_PCA)
plot(tree3.Customers)
text(tree3.Customers, pretty=1, cex = 0.7)
cv3.Customers = cv.tree(tree3.Customers, FUN=prune.misclass)
cv3.Customers$size
## [1] 14 10 8 5 4 3 2 1
cv3.Customers$dev
## [1] 126 126 130 137 141 195 229 308
# Prune the tree for cluster 3
prune3.Customers = prune.misclass(tree3.Customers, best=5)
plot(prune3.Customers)
text(prune3.Customers, pretty=1, cex = 0.7)
sum(Customers_cleaned$Response == 1)
## [1] 329
sum(Customers_cleaned$Response == 0)
## [1] 1869
glm.fits = glm(Response ~ Education + Income + NumChildren + Recency + NumDealsPurchases + NumWebPurchases + NumStorePurchases + YearsJoined + Relationship + Age + Spending + TotalAcceptedCmp, data = Customers_cleaned, family = binomial)
summary(glm.fits)
##
## Call:
## glm(formula = Response ~ Education + Income + NumChildren + Recency +
## NumDealsPurchases + NumWebPurchases + NumStorePurchases +
## YearsJoined + Relationship + Age + Spending + TotalAcceptedCmp,
## family = binomial, data = Customers_cleaned)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.253e+01 1.708e+00 -7.333 2.25e-13 ***
## Education2 7.579e-01 4.370e-01 1.734 0.082875 .
## Education3 1.093e+00 4.895e-01 2.232 0.025598 *
## Education4 1.658e+00 4.721e-01 3.512 0.000444 ***
## Income 6.088e-07 1.159e-05 0.053 0.958093
## NumChildren -6.878e-01 2.262e-01 -3.040 0.002363 **
## Recency -3.798e-02 4.534e-03 -8.376 < 2e-16 ***
## NumDealsPurchases 1.917e-01 6.604e-02 2.902 0.003704 **
## NumWebPurchases 6.584e-02 4.733e-02 1.391 0.164188
## NumStorePurchases -2.446e-01 5.250e-02 -4.659 3.18e-06 ***
## YearsJoined 1.525e+00 1.849e-01 8.249 < 2e-16 ***
## Relationship -1.534e+00 2.339e-01 -6.557 5.49e-11 ***
## Age 9.480e-04 9.792e-03 0.097 0.922872
## Spending -4.803e-04 4.020e-04 -1.195 0.232139
## TotalAcceptedCmp 3.450e+00 2.080e-01 16.584 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1855.80 on 2197 degrees of freedom
## Residual deviance: 572.21 on 2183 degrees of freedom
## AIC: 602.21
##
## Number of Fisher Scoring iterations: 7
We now remove the insignificant variables one by one
glm.fits1 = glm(Response ~ Education + NumChildren + Recency + NumDealsPurchases + NumWebPurchases + NumStorePurchases + YearsJoined + Relationship + Age + Spending + TotalAcceptedCmp, data = Customers_cleaned, family = binomial)
summary(glm.fits1)
##
## Call:
## glm(formula = Response ~ Education + NumChildren + Recency +
## NumDealsPurchases + NumWebPurchases + NumStorePurchases +
## YearsJoined + Relationship + Age + Spending + TotalAcceptedCmp,
## family = binomial, data = Customers_cleaned)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.250e+01 1.624e+00 -7.696 1.41e-14 ***
## Education2 7.613e-01 4.322e-01 1.762 0.078136 .
## Education3 1.095e+00 4.866e-01 2.251 0.024392 *
## Education4 1.661e+00 4.688e-01 3.543 0.000395 ***
## NumChildren -6.850e-01 2.200e-01 -3.114 0.001845 **
## Recency -3.798e-02 4.534e-03 -8.377 < 2e-16 ***
## NumDealsPurchases 1.906e-01 6.307e-02 3.023 0.002506 **
## NumWebPurchases 6.613e-02 4.691e-02 1.410 0.158625
## NumStorePurchases -2.439e-01 5.071e-02 -4.809 1.52e-06 ***
## YearsJoined 1.523e+00 1.802e-01 8.448 < 2e-16 ***
## Relationship -1.534e+00 2.338e-01 -6.560 5.37e-11 ***
## Age 1.008e-03 9.724e-03 0.104 0.917423
## Spending -4.655e-04 2.872e-04 -1.621 0.104980
## TotalAcceptedCmp 3.450e+00 2.080e-01 16.591 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1855.80 on 2197 degrees of freedom
## Residual deviance: 572.22 on 2184 degrees of freedom
## AIC: 600.22
##
## Number of Fisher Scoring iterations: 7
glm.fits2 = glm(Response ~ Education + NumChildren + Recency + NumDealsPurchases + NumStorePurchases + YearsJoined + Relationship + Age + Spending + TotalAcceptedCmp, data = Customers_cleaned, family = binomial)
summary(glm.fits2)
##
## Call:
## glm(formula = Response ~ Education + NumChildren + Recency +
## NumDealsPurchases + NumStorePurchases + YearsJoined + Relationship +
## Age + Spending + TotalAcceptedCmp, family = binomial, data = Customers_cleaned)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.250e+01 1.610e+00 -7.765 8.15e-15 ***
## Education2 7.443e-01 4.294e-01 1.733 0.083054 .
## Education3 1.055e+00 4.832e-01 2.183 0.029008 *
## Education4 1.670e+00 4.658e-01 3.586 0.000336 ***
## NumChildren -6.846e-01 2.184e-01 -3.135 0.001719 **
## Recency -3.790e-02 4.537e-03 -8.353 < 2e-16 ***
## NumDealsPurchases 2.118e-01 6.035e-02 3.510 0.000449 ***
## NumStorePurchases -2.339e-01 5.009e-02 -4.671 3.00e-06 ***
## YearsJoined 1.527e+00 1.787e-01 8.547 < 2e-16 ***
## Relationship -1.528e+00 2.330e-01 -6.560 5.39e-11 ***
## Age 2.586e-03 9.658e-03 0.268 0.788881
## Spending -3.580e-04 2.739e-04 -1.307 0.191235
## TotalAcceptedCmp 3.445e+00 2.069e-01 16.652 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1855.80 on 2197 degrees of freedom
## Residual deviance: 574.11 on 2185 degrees of freedom
## AIC: 600.11
##
## Number of Fisher Scoring iterations: 7
glm.fits3 = glm(Response ~ Education + NumChildren + Recency + NumDealsPurchases + NumStorePurchases + YearsJoined + Relationship + Spending + TotalAcceptedCmp, data = Customers_cleaned, family = binomial)
summary(glm.fits3)
##
## Call:
## glm(formula = Response ~ Education + NumChildren + Recency +
## NumDealsPurchases + NumStorePurchases + YearsJoined + Relationship +
## Spending + TotalAcceptedCmp, family = binomial, data = Customers_cleaned)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.238e+01 1.545e+00 -8.015 1.10e-15 ***
## Education2 7.572e-01 4.265e-01 1.775 0.075831 .
## Education3 1.072e+00 4.792e-01 2.236 0.025329 *
## Education4 1.685e+00 4.623e-01 3.645 0.000267 ***
## NumChildren -6.749e-01 2.156e-01 -3.131 0.001744 **
## Recency -3.794e-02 4.538e-03 -8.361 < 2e-16 ***
## NumDealsPurchases 2.112e-01 6.038e-02 3.498 0.000468 ***
## NumStorePurchases -2.331e-01 4.997e-02 -4.664 3.11e-06 ***
## YearsJoined 1.526e+00 1.787e-01 8.543 < 2e-16 ***
## Relationship -1.533e+00 2.324e-01 -6.598 4.15e-11 ***
## Spending -3.488e-04 2.717e-04 -1.284 0.199204
## TotalAcceptedCmp 3.444e+00 2.069e-01 16.645 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1855.80 on 2197 degrees of freedom
## Residual deviance: 574.18 on 2186 degrees of freedom
## AIC: 598.18
##
## Number of Fisher Scoring iterations: 7
glm.fits4 = glm(Response ~ Education + NumChildren + Recency + NumDealsPurchases + NumStorePurchases + YearsJoined + Relationship + TotalAcceptedCmp, data = Customers_cleaned, family = binomial)
summary(glm.fits4)
##
## Call:
## glm(formula = Response ~ Education + NumChildren + Recency +
## NumDealsPurchases + NumStorePurchases + YearsJoined + Relationship +
## TotalAcceptedCmp, family = binomial, data = Customers_cleaned)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -12.252265 1.537240 -7.970 1.58e-15 ***
## Education2 0.694876 0.422692 1.644 0.100191
## Education3 1.010858 0.475816 2.124 0.033630 *
## Education4 1.630891 0.458252 3.559 0.000372 ***
## NumChildren -0.567129 0.196436 -2.887 0.003888 **
## Recency -0.038237 0.004516 -8.467 < 2e-16 ***
## NumDealsPurchases 0.208783 0.059274 3.522 0.000428 ***
## NumStorePurchases -0.266813 0.042675 -6.252 4.05e-10 ***
## YearsJoined 1.509965 0.177595 8.502 < 2e-16 ***
## Relationship -1.538676 0.231947 -6.634 3.27e-11 ***
## TotalAcceptedCmp 3.369045 0.195940 17.194 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1855.80 on 2197 degrees of freedom
## Residual deviance: 575.86 on 2187 degrees of freedom
## AIC: 597.86
##
## Number of Fisher Scoring iterations: 7
Predicting the ‘Reponse’ variable using all the data
glm.probs = predict(glm.fits4, type = "response")
glm.pred = rep(0, 2198)
glm.pred[glm.probs > 0.5] = 1
table(glm.pred, as.factor(Customers_cleaned$Response))
##
## glm.pred 0 1
## 0 1821 77
## 1 48 252
mean(glm.pred == Customers_cleaned$Response)
## [1] 0.9431301
Our logistic regression model correctly predicts the response variable 94.3% of the time.
We now split into training and testing data
set.seed(123)
# Subset a dataframe with only response = 1
Customers_cleaned_Response1 <- subset(Customers_cleaned, Response == 1)
Customers_cleaned_Response0 <- subset(Customers_cleaned, Response == 0)
dim(Customers_cleaned_Response1) #329
## [1] 329 37
# We subset a dataframe with only response = 0 and then random sample into equal size with response = 1
Customers_cleaned_Response0_ind <- sample(1:nrow(Customers_cleaned_Response0), nrow(Customers_cleaned_Response1))
Customers_cleaned_Response0 <- Customers_cleaned_Response0[Customers_cleaned_Response0_ind, ]
# Merge
train <- rbind(Customers_cleaned_Response1, Customers_cleaned_Response0)
train_ind <- sample(1:nrow(train), nrow(train)*0.75)
train <- Customers_cleaned[train_ind, ]
# Extract the remaining observations as testing data
test <- Customers_cleaned[-train_ind, ]
# Re-fit the logistic regression model
glm.fits5 = glm(Response ~ Education + NumChildren + Recency + NumDealsPurchases + NumStorePurchases + YearsJoined + Relationship + TotalAcceptedCmp, data = train, family = binomial)
# Result
summary(glm.fits5)
##
## Call:
## glm(formula = Response ~ Education + NumChildren + Recency +
## NumDealsPurchases + NumStorePurchases + YearsJoined + Relationship +
## TotalAcceptedCmp, family = binomial, data = train)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -14.28008 4.14399 -3.446 0.000569 ***
## Education2 1.48484 1.01416 1.464 0.143163
## Education3 2.37658 1.21590 1.955 0.050631 .
## Education4 2.10854 1.21319 1.738 0.082208 .
## NumChildren -1.32332 0.61756 -2.143 0.032129 *
## Recency -0.04154 0.01341 -3.099 0.001942 **
## NumDealsPurchases 0.28165 0.15016 1.876 0.060694 .
## NumStorePurchases -0.40243 0.12095 -3.327 0.000877 ***
## YearsJoined 1.76272 0.47385 3.720 0.000199 ***
## Relationship -1.88713 0.67219 -2.807 0.004994 **
## TotalAcceptedCmp 4.42919 0.62431 7.095 1.3e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 384.422 on 492 degrees of freedom
## Residual deviance: 87.701 on 482 degrees of freedom
## AIC: 109.7
##
## Number of Fisher Scoring iterations: 8
# Prediction
glm.probs2 = predict(glm.fits5, newdata = test, type = "response")
glm.pred2 <- ifelse(glm.probs2 > 0.5, 1, 0)
table(glm.pred2, as.factor(test$Response))
##
## glm.pred2 0 1
## 0 1397 64
## 1 44 200
# Accuracy
mean(glm.pred2 == test$Response)
## [1] 0.9366569
Load relevant libraries
library(arules)
## Loading required package: Matrix
##
## Attaching package: 'Matrix'
## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack
##
## Attaching package: 'arules'
## The following object is masked from 'package:dplyr':
##
## recode
## The following objects are masked from 'package:base':
##
## abbreviate, write
library(effects)
## Loading required package: carData
## lattice theme set by effectsTheme()
## See ?effectsTheme for details.
library(arulesViz)
# Extract the relevant features
CustomersAssoc1 <- Customers_cleaned[c("AgeCategory", "NumChildren", "Education", "Relationship", "Recency", "YearsJoined", "NumWebPurchases")]
# Convert into categorical variables using quantiles
CustomersAssoc1$NumWebPurchases <- cut(
CustomersAssoc1$NumWebPurchases,
breaks = quantile(CustomersAssoc1$NumWebPurchases, c(0, 0.33, 0.66, 1)),
labels = c("Low", "Medium", "High"),
include.lowest = TRUE
)
CustomersAssoc1$Recency <- cut(
CustomersAssoc1$Recency,
breaks = quantile(CustomersAssoc1$Recency, c(0, 0.5, 1)),
labels = c("Recent", "Distant"),
include.lowest = TRUE
)
CustomersAssoc1$YearsJoined <- cut(
CustomersAssoc1$YearsJoined,
breaks = quantile(CustomersAssoc1$YearsJoined, c(0, 0.5, 1)),
labels = c("<8 years", ">8 years"),
include.lowest = TRUE
)
CustomersAssoc1$NumChildren <- ifelse(CustomersAssoc1$NumChildren == 0,"NoChild", "YesChild")
CustomersAssoc1$AgeCategory <- ifelse(CustomersAssoc1$AgeCategory == 1,"Millenials",
ifelse(CustomersAssoc1$AgeCategory == 2, "GenX", "BabyBoomer"))
CustomersAssoc1$Relationship <- ifelse(CustomersAssoc1$Relationship == 1,"Not-Partnered", "Partnered")
CustomersAssoc1$Education <- ifelse(CustomersAssoc1$Education == 1,"Bachelors",
ifelse(CustomersAssoc1$Education == 2, "Graduates",
ifelse(CustomersAssoc1$Education ==3, "Masters", "PhDs")))
# Association rules for web channel
rules_web <- apriori(CustomersAssoc1, parameter = list(support = 0.05, confidence = 0.3), appearance = list(rhs = "NumWebPurchases=High"))
## Warning: Column(s) 1, 2, 3, 4 not logical or factor. Applying default
## discretization (see '? discretizeDF').
## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.3 0.1 1 none FALSE TRUE 5 0.05 1
## maxlen target ext
## 10 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 109
##
## set item appearances ...[1 item(s)] done [0.00s].
## set transactions ...[18 item(s), 2198 transaction(s)] done [0.00s].
## sorting and recoding items ... [18 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 5 6 done [0.00s].
## writing ... [17 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].
inspect(rules_web)
## lhs rhs support confidence coverage lift count
## [1] {Education=PhDs} => {NumWebPurchases=High} 0.07051865 0.3283898 0.2147407 1.171755 155
## [2] {YearsJoined=>8 years} => {NumWebPurchases=High} 0.08007279 0.3606557 0.2220200 1.286885 176
## [3] {AgeCategory=BabyBoomer} => {NumWebPurchases=High} 0.11692448 0.3346354 0.3494086 1.194040 257
## [4] {NumChildren=YesChild,
## Education=PhDs} => {NumWebPurchases=High} 0.05186533 0.3294798 0.1574158 1.175644 114
## [5] {Education=PhDs,
## YearsJoined=<8 years} => {NumWebPurchases=High} 0.05050045 0.3016304 0.1674249 1.076272 111
## [6] {Relationship=Partnered,
## YearsJoined=>8 years} => {NumWebPurchases=High} 0.05277525 0.3741935 0.1410373 1.335191 116
## [7] {NumChildren=YesChild,
## YearsJoined=>8 years} => {NumWebPurchases=High} 0.05914468 0.3757225 0.1574158 1.340646 130
## [8] {AgeCategory=BabyBoomer,
## Recency=Distant} => {NumWebPurchases=High} 0.05914468 0.3194103 0.1851683 1.139714 130
## [9] {AgeCategory=BabyBoomer,
## Recency=Recent} => {NumWebPurchases=High} 0.05777980 0.3518006 0.1642402 1.255288 127
## [10] {AgeCategory=BabyBoomer,
## Education=Graduates} => {NumWebPurchases=High} 0.05095541 0.3043478 0.1674249 1.085968 112
## [11] {AgeCategory=BabyBoomer,
## Relationship=Partnered} => {NumWebPurchases=High} 0.07142857 0.3230453 0.2211101 1.152684 157
## [12] {AgeCategory=BabyBoomer,
## NumChildren=YesChild} => {NumWebPurchases=High} 0.08553230 0.3686275 0.2320291 1.315330 188
## [13] {AgeCategory=BabyBoomer,
## YearsJoined=<8 years} => {NumWebPurchases=High} 0.08644222 0.3130148 0.2761601 1.116894 190
## [14] {AgeCategory=BabyBoomer,
## NumChildren=YesChild,
## Relationship=Partnered} => {NumWebPurchases=High} 0.05641492 0.3746224 0.1505914 1.336721 124
## [15] {AgeCategory=BabyBoomer,
## Relationship=Partnered,
## YearsJoined=<8 years} => {NumWebPurchases=High} 0.05368517 0.3072917 0.1747043 1.096473 118
## [16] {AgeCategory=BabyBoomer,
## NumChildren=YesChild,
## YearsJoined=<8 years} => {NumWebPurchases=High} 0.06278435 0.3424318 0.1833485 1.221859 138
## [17] {NumChildren=YesChild,
## Relationship=Partnered,
## Recency=Distant} => {NumWebPurchases=High} 0.07370337 0.3079848 0.2393085 1.098946 162
# Subset the relevant variables for the second association rule
CustomersAssoc2 <- subset(CustomersAssoc1, select = -NumWebPurchases)
CustomersAssoc2$NumStorePurchases <- Customers_cleaned$NumStorePurchases
CustomersAssoc2$NumStorePurchases <- cut(
CustomersAssoc2$NumStorePurchases,
breaks = quantile(CustomersAssoc2$NumStorePurchases, c(0, 0.33, 0.66, 1)),
labels = c("Low", "Medium", "High"),
include.lowest = TRUE
)
rules_store <- apriori(CustomersAssoc2, parameter = list(support = 0.05, confidence = 0.4), appearance = list(rhs = "NumStorePurchases=High"))
## Warning: Column(s) 1, 2, 3, 4 not logical or factor. Applying default
## discretization (see '? discretizeDF').
## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.4 0.1 1 none FALSE TRUE 5 0.05 1
## maxlen target ext
## 10 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 109
##
## set item appearances ...[1 item(s)] done [0.00s].
## set transactions ...[18 item(s), 2198 transaction(s)] done [0.00s].
## sorting and recoding items ... [18 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 5 6 done [0.00s].
## writing ... [9 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].
inspect(rules_store)
## lhs rhs support confidence coverage lift count
## [1] {NumChildren=NoChild} => {NumStorePurchases=High} 0.12602366 0.4460548 0.2825296 1.531919 277
## [2] {AgeCategory=BabyBoomer,
## NumChildren=NoChild} => {NumStorePurchases=High} 0.05141037 0.4379845 0.1173794 1.504203 113
## [3] {NumChildren=NoChild,
## Relationship=Not-Partnered} => {NumStorePurchases=High} 0.05414013 0.4817814 0.1123749 1.654618 119
## [4] {NumChildren=NoChild,
## Recency=Distant} => {NumStorePurchases=High} 0.06414923 0.4563107 0.1405823 1.567142 141
## [5] {NumChildren=NoChild,
## Recency=Recent} => {NumStorePurchases=High} 0.06187443 0.4358974 0.1419472 1.497035 136
## [6] {NumChildren=NoChild,
## Education=Graduates} => {NumStorePurchases=High} 0.06187443 0.4317460 0.1433121 1.482778 136
## [7] {NumChildren=NoChild,
## Relationship=Partnered} => {NumStorePurchases=High} 0.07188353 0.4224599 0.1701547 1.450886 158
## [8] {NumChildren=NoChild,
## YearsJoined=<8 years} => {NumStorePurchases=High} 0.09463148 0.4342380 0.2179254 1.491336 208
## [9] {NumChildren=NoChild,
## Relationship=Partnered,
## YearsJoined=<8 years} => {NumStorePurchases=High} 0.05595996 0.4226804 0.1323931 1.451643 123
CustomersAssoc3 <- subset(CustomersAssoc1, select = -NumWebPurchases)
CustomersAssoc3$NumCatalogPurchases <- Customers_cleaned$NumCatalogPurchases
CustomersAssoc3$NumCatalogPurchases <- cut(
CustomersAssoc3$NumCatalogPurchases,
breaks = quantile(CustomersAssoc3$NumCatalogPurchases, c(0, 0.33, 0.66, 1)),
labels = c("Low", "Medium", "High"),
include.lowest = TRUE
)
rules_catalog <- apriori(CustomersAssoc3, parameter = list(support = 0.05, confidence = 0.6), appearance = list(rhs = "NumCatalogPurchases=High"))
## Warning: Column(s) 1, 2, 3, 4 not logical or factor. Applying default
## discretization (see '? discretizeDF').
## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.6 0.1 1 none FALSE TRUE 5 0.05 1
## maxlen target ext
## 10 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 109
##
## set item appearances ...[1 item(s)] done [0.00s].
## set transactions ...[18 item(s), 2198 transaction(s)] done [0.00s].
## sorting and recoding items ... [18 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 5 6 done [0.00s].
## writing ... [19 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].
inspect(rules_catalog)
## lhs rhs support confidence coverage lift count
## [1] {NumChildren=NoChild} => {NumCatalogPurchases=High} 0.18471338 0.6537842 0.28252957 2.103979 406
## [2] {AgeCategory=BabyBoomer,
## NumChildren=NoChild} => {NumCatalogPurchases=High} 0.08052775 0.6860465 0.11737944 2.207804 177
## [3] {NumChildren=NoChild,
## Relationship=Not-Partnered} => {NumCatalogPurchases=High} 0.07233849 0.6437247 0.11237489 2.071606 159
## [4] {AgeCategory=GenX,
## NumChildren=NoChild} => {NumCatalogPurchases=High} 0.05823476 0.6701571 0.08689718 2.156669 128
## [5] {NumChildren=NoChild,
## Recency=Distant} => {NumCatalogPurchases=High} 0.09508644 0.6763754 0.14058235 2.176681 209
## [6] {NumChildren=NoChild,
## Recency=Recent} => {NumCatalogPurchases=High} 0.08962693 0.6314103 0.14194722 2.031976 197
## [7] {NumChildren=NoChild,
## Education=Graduates} => {NumCatalogPurchases=High} 0.09554140 0.6666667 0.14331210 2.145437 210
## [8] {NumChildren=NoChild,
## Relationship=Partnered} => {NumCatalogPurchases=High} 0.11237489 0.6604278 0.17015469 2.125359 247
## [9] {NumChildren=NoChild,
## YearsJoined=<8 years} => {NumCatalogPurchases=High} 0.14285714 0.6555324 0.21792539 2.109605 314
## [10] {AgeCategory=BabyBoomer,
## NumChildren=NoChild,
## YearsJoined=<8 years} => {NumCatalogPurchases=High} 0.06505914 0.7009804 0.09281165 2.255864 143
## [11] {NumChildren=NoChild,
## Relationship=Not-Partnered,
## YearsJoined=<8 years} => {NumCatalogPurchases=High} 0.05414013 0.6329787 0.08553230 2.037024 119
## [12] {NumChildren=NoChild,
## Education=Graduates,
## Recency=Distant} => {NumCatalogPurchases=High} 0.05095541 0.6913580 0.07370337 2.224897 112
## [13] {NumChildren=NoChild,
## Relationship=Partnered,
## Recency=Distant} => {NumCatalogPurchases=High} 0.05505005 0.6875000 0.08007279 2.212482 121
## [14] {NumChildren=NoChild,
## Recency=Distant,
## YearsJoined=<8 years} => {NumCatalogPurchases=High} 0.07324841 0.6880342 0.10646042 2.214201 161
## [15] {NumChildren=NoChild,
## Relationship=Partnered,
## Recency=Recent} => {NumCatalogPurchases=High} 0.05732484 0.6363636 0.09008189 2.047917 126
## [16] {NumChildren=NoChild,
## Recency=Recent,
## YearsJoined=<8 years} => {NumCatalogPurchases=High} 0.06960874 0.6244898 0.11146497 2.009705 153
## [17] {NumChildren=NoChild,
## Education=Graduates,
## Relationship=Partnered} => {NumCatalogPurchases=High} 0.05868972 0.6861702 0.08553230 2.208202 129
## [18] {NumChildren=NoChild,
## Education=Graduates,
## YearsJoined=<8 years} => {NumCatalogPurchases=High} 0.07734304 0.6772908 0.11419472 2.179627 170
## [19] {NumChildren=NoChild,
## Relationship=Partnered,
## YearsJoined=<8 years} => {NumCatalogPurchases=High} 0.08871702 0.6701031 0.13239308 2.156496 195